[{"title":"Adaptive, Synchronous, and Mobile Online Education: Developing the ASYMPTOTE Learning Environment","volume":10,"date_created":"2025-12-17T08:53:34Z","author":[{"first_name":"S","full_name":"Barlovits, S","last_name":"Barlovits"},{"first_name":"A","last_name":"Caldeira","full_name":"Caldeira, A"},{"first_name":"G","full_name":"Fesakis, G","last_name":"Fesakis"},{"first_name":"S","full_name":"Jablonski, S","last_name":"Jablonski"},{"full_name":"Filippaki, DK","last_name":"Filippaki","first_name":"DK"},{"full_name":"Lázaro, C","last_name":"Lázaro","first_name":"C"},{"first_name":"M","full_name":"Ludwig, M","last_name":"Ludwig"},{"first_name":"MF","last_name":"Mammana","full_name":"Mammana, MF"},{"first_name":"A","last_name":"Moura","full_name":"Moura, A"},{"last_name":"Oehler","full_name":"Oehler, DXK","first_name":"DXK"},{"full_name":"Recio, T","last_name":"Recio","first_name":"T"},{"last_name":"Taranto","full_name":"Taranto, E","first_name":"E"},{"first_name":"S","full_name":"Volika, S","last_name":"Volika"}],"date_updated":"2025-12-17T08:56:18Z","intvolume":" 10","citation":{"ieee":"S. Barlovits et al., “Adaptive, Synchronous, and Mobile Online Education: Developing the ASYMPTOTE Learning Environment,” vol. 10, no. 10, 2022.","chicago":"Barlovits, S, A Caldeira, G Fesakis, S Jablonski, DK Filippaki, C Lázaro, M Ludwig, et al. “Adaptive, Synchronous, and Mobile Online Education: Developing the ASYMPTOTE Learning Environment” 10, no. 10 (2022).","ama":"Barlovits S, Caldeira A, Fesakis G, et al. Adaptive, Synchronous, and Mobile Online Education: Developing the ASYMPTOTE Learning Environment. 2022;10(10).","mla":"Barlovits, S., et al. Adaptive, Synchronous, and Mobile Online Education: Developing the ASYMPTOTE Learning Environment. no. 10, 2022.","short":"S. Barlovits, A. Caldeira, G. Fesakis, S. Jablonski, D. Filippaki, C. Lázaro, M. Ludwig, M. Mammana, A. Moura, D. Oehler, T. Recio, E. Taranto, S. Volika, 10 (2022).","bibtex":"@article{Barlovits_Caldeira_Fesakis_Jablonski_Filippaki_Lázaro_Ludwig_Mammana_Moura_Oehler_et al._2022, title={Adaptive, Synchronous, and Mobile Online Education: Developing the ASYMPTOTE Learning Environment}, volume={10}, number={10}, author={Barlovits, S and Caldeira, A and Fesakis, G and Jablonski, S and Filippaki, DK and Lázaro, C and Ludwig, M and Mammana, MF and Moura, A and Oehler, DXK and et al.}, year={2022} }","apa":"Barlovits, S., Caldeira, A., Fesakis, G., Jablonski, S., Filippaki, D., Lázaro, C., Ludwig, M., Mammana, M., Moura, A., Oehler, D., Recio, T., Taranto, E., & Volika, S. (2022). Adaptive, Synchronous, and Mobile Online Education: Developing the ASYMPTOTE Learning Environment. 10(10)."},"year":"2022","issue":"10","quality_controlled":"1","publication_identifier":{"issn":["2227-7390"]},"publication_status":"published","user_id":"111489","_id":"63175","status":"public","type":"journal_article"},{"type":"journal_article","status":"public","user_id":"111489","_id":"63174","issue":"5","publication_status":"published","publication_identifier":{"issn":["2227-7102"]},"quality_controlled":"1","citation":{"apa":"Barbosa, A., Vale, I., Jablonski, S., & Ludwig, M. (2022). Walking through Algebraic Thinking with Theme-Based (Mobile) Math Trails. 12(5).","bibtex":"@article{Barbosa_Vale_Jablonski_Ludwig_2022, title={Walking through Algebraic Thinking with Theme-Based (Mobile) Math Trails}, volume={12}, number={5}, author={Barbosa, A and Vale, I and Jablonski, S and Ludwig, M}, year={2022} }","short":"A. Barbosa, I. Vale, S. Jablonski, M. Ludwig, 12 (2022).","mla":"Barbosa, A., et al. Walking through Algebraic Thinking with Theme-Based (Mobile) Math Trails. no. 5, 2022.","ieee":"A. Barbosa, I. Vale, S. Jablonski, and M. Ludwig, “Walking through Algebraic Thinking with Theme-Based (Mobile) Math Trails,” vol. 12, no. 5, 2022.","chicago":"Barbosa, A, I Vale, S Jablonski, and M Ludwig. “Walking through Algebraic Thinking with Theme-Based (Mobile) Math Trails” 12, no. 5 (2022).","ama":"Barbosa A, Vale I, Jablonski S, Ludwig M. Walking through Algebraic Thinking with Theme-Based (Mobile) Math Trails. 2022;12(5)."},"intvolume":" 12","year":"2022","author":[{"first_name":"A","last_name":"Barbosa","full_name":"Barbosa, A"},{"first_name":"I","full_name":"Vale, I","last_name":"Vale"},{"first_name":"S","full_name":"Jablonski, S","last_name":"Jablonski"},{"first_name":"M","last_name":"Ludwig","full_name":"Ludwig, M"}],"date_created":"2025-12-17T08:53:34Z","volume":12,"date_updated":"2025-12-17T08:56:22Z","title":"Walking through Algebraic Thinking with Theme-Based (Mobile) Math Trails"},{"department":[{"_id":"233"},{"_id":"716"}],"user_id":"90389","series_title":" Münsteraner Schriften zur zeitgenössischen Musik","_id":"36424","language":[{"iso":"ger"}],"type":"book","status":"public","abstract":[{"lang":"eng","text":"Das Oratorium kann als wichtige Gattung für die Analyse des Zusammenspiels von Religion und Politik im Medium der Musik gelten. Die Studie wendet sich dem Verhältnis dieser religiösen Musikform zum deutschen Nationalismus vom Beginn des Ersten bis zum Ende des Zweiten Weltkriegs zu. Im Fokus stehen verschiedene Weisen der Instrumentalisierung von Musik, etwa zur ‚Heldenehrung‘, zur Bildung einer ‚vorgestellten Gemeinschaft‘ oder zur Gewinnung der Arbeiterschaft. Bei der Analyse der Politisierung des Oratoriums sind vier Beobachtungsperspektiven leitend: Konfession, Säkularisierung, Erinnerungskultur und Vergemeinschaftung.\r\n\r\nEntsprechend liegt der Schwerpunkt der Studie auf der Analyse der sozialgeschichtlichen Funktion der Gattung. Daneben jedoch werden – in Form von Fallstudien zu bisher unerforschten Werken – auch musikalische Detailanalysen durchgeführt, die das in der jeweiligen Komposition realisierte Verhältnis von religiösen und nationalistischen Elementen offenlegen. "}],"volume":8,"date_created":"2023-01-12T12:43:47Z","author":[{"first_name":"Dominik","full_name":"Höink, Dominik","id":"90389","last_name":"Höink"}],"date_updated":"2025-12-17T09:00:36Z","publisher":"Waxmann Verlag","title":"Oratorium und Nation (1914–1945) ","publication_identifier":{"isbn":["978-3-8309-3984-9"]},"publication_status":"published","intvolume":" 8","page":"590","citation":{"mla":"Höink, Dominik. Oratorium und Nation (1914–1945) . Waxmann Verlag, 2022.","short":"D. Höink, Oratorium und Nation (1914–1945) , Waxmann Verlag, Münster, 2022.","bibtex":"@book{Höink_2022, place={Münster}, series={ Münsteraner Schriften zur zeitgenössischen Musik}, title={Oratorium und Nation (1914–1945) }, volume={8}, publisher={Waxmann Verlag}, author={Höink, Dominik}, year={2022}, collection={ Münsteraner Schriften zur zeitgenössischen Musik} }","apa":"Höink, D. (2022). Oratorium und Nation (1914–1945) (Vol. 8). Waxmann Verlag.","ama":"Höink D. Oratorium und Nation (1914–1945) . Vol 8. Waxmann Verlag; 2022.","chicago":"Höink, Dominik. Oratorium und Nation (1914–1945) . Vol. 8. Münsteraner Schriften zur zeitgenössischen Musik. Münster: Waxmann Verlag, 2022.","ieee":"D. Höink, Oratorium und Nation (1914–1945) , vol. 8. Münster: Waxmann Verlag, 2022."},"year":"2022","place":"Münster"},{"publication":"Époque Émilienne Philosophy and Science in the Age of Émilie Du Châtelet (1706-1749)","abstract":[{"text":"n 1789, Eberhard repudiated Kant’s claim expressed in the first edition of his Critique of Pure Reason to have delivered a new, namely transcendental turn in philosophy, as he was able to retrace our cognition to the origin of phenomena instead of delivering a “merely logical deduction”. Eberhard holds that there was nothing new, but all delivered in Leibniz and Wolff; to prove his claim he refers to a quote from Du Châtelet, taken from a paragraph where she determines the right understanding as to be able “to penetrate to the origin of phenomena”. This paper brings Du Châtelet into discourse with Kant via this Eberhard quote. In its first part, it investigates the use of her quote in the Kant-Eberhard controversy. The second part serves to ground the quote in Du Châtelet’s epistemology. It lays out how to understand Du Châtelet’s claim to penetrate to the origin of phenomena. Du Châtelet’s claim to have renewed philosophy must be taken seriously, and it is helpful for rethinking the German philosophical development from the rationalists to Kant through including Du Châtelet’s theory of cognition.","lang":"eng"}],"language":[{"iso":"eng"}],"keyword":["Émilie Du Châtelet","History of Science","Newton","Kant","Eberhard","Wolff","Leibniz"],"quality_controlled":"1","year":"2022","date_created":"2022-12-21T11:35:14Z","publisher":"Springer International Publishing","title":"Du Châtelet and Kant: Claiming the Renewal of Philosophy","type":"book_chapter","status":"public","editor":[{"full_name":"Hagengruber, Ruth Edith","last_name":"Hagengruber","first_name":"Ruth Edith"}],"user_id":"91827","series_title":"Women in the History of Philosophy and Science ","department":[{"_id":"615"},{"_id":"14"},{"_id":"519"}],"_id":"34705","publication_status":"published","publication_identifier":{"isbn":["9783030899202","9783030899219"],"issn":["2523-8760","2523-8779"]},"citation":{"apa":"Hagengruber, R. E. (2022). Du Châtelet and Kant: Claiming the Renewal of Philosophy. In R. E. Hagengruber (Ed.), Époque Émilienne Philosophy and Science in the Age of Émilie Du Châtelet (1706-1749) (Vol. 10, pp. 57–84). Springer International Publishing. https://doi.org/10.1007/978-3-030-89921-9_3","bibtex":"@inbook{Hagengruber_2022, place={Cham}, series={Women in the History of Philosophy and Science }, title={Du Châtelet and Kant: Claiming the Renewal of Philosophy}, volume={10}, DOI={10.1007/978-3-030-89921-9_3}, booktitle={Époque Émilienne Philosophy and Science in the Age of Émilie Du Châtelet (1706-1749)}, publisher={Springer International Publishing}, author={Hagengruber, Ruth Edith}, editor={Hagengruber, Ruth Edith}, year={2022}, pages={57–84}, collection={Women in the History of Philosophy and Science } }","mla":"Hagengruber, Ruth Edith. “Du Châtelet and Kant: Claiming the Renewal of Philosophy.” Époque Émilienne Philosophy and Science in the Age of Émilie Du Châtelet (1706-1749), edited by Ruth Edith Hagengruber, vol. 10, Springer International Publishing, 2022, pp. 57–84, doi:10.1007/978-3-030-89921-9_3.","short":"R.E. Hagengruber, in: R.E. Hagengruber (Ed.), Époque Émilienne Philosophy and Science in the Age of Émilie Du Châtelet (1706-1749), Springer International Publishing, Cham, 2022, pp. 57–84.","ama":"Hagengruber RE. Du Châtelet and Kant: Claiming the Renewal of Philosophy. In: Hagengruber RE, ed. Époque Émilienne Philosophy and Science in the Age of Émilie Du Châtelet (1706-1749). Vol 10. Women in the History of Philosophy and Science . Springer International Publishing; 2022:57-84. doi:10.1007/978-3-030-89921-9_3","chicago":"Hagengruber, Ruth Edith. “Du Châtelet and Kant: Claiming the Renewal of Philosophy.” In Époque Émilienne Philosophy and Science in the Age of Émilie Du Châtelet (1706-1749), edited by Ruth Edith Hagengruber, 10:57–84. Women in the History of Philosophy and Science . Cham: Springer International Publishing, 2022. https://doi.org/10.1007/978-3-030-89921-9_3.","ieee":"R. E. Hagengruber, “Du Châtelet and Kant: Claiming the Renewal of Philosophy,” in Époque Émilienne Philosophy and Science in the Age of Émilie Du Châtelet (1706-1749), vol. 10, R. E. Hagengruber, Ed. Cham: Springer International Publishing, 2022, pp. 57–84."},"intvolume":" 10","page":"57-84","place":"Cham","author":[{"first_name":"Ruth Edith","orcid":"https://orcid.org/0000-0003-3360-6335","last_name":"Hagengruber","full_name":"Hagengruber, Ruth Edith","id":"198"}],"volume":10,"date_updated":"2025-12-17T13:40:24Z","doi":"10.1007/978-3-030-89921-9_3"},{"_id":"63184","series_title":"Women in the History of Philosophy and Science ","user_id":"91827","department":[{"_id":"14"}],"editor":[{"last_name":"Hagengruber","full_name":"Hagengruber, Ruth Edith","first_name":"Ruth Edith"}],"status":"public","type":"book_chapter","doi":"10.1007/978-3-030-89921-9_1","date_updated":"2025-12-17T13:38:49Z","author":[{"orcid":"https://orcid.org/0000-0003-3360-6335","last_name":"Hagengruber","full_name":"Hagengruber, Ruth","id":"198","first_name":"Ruth"}],"volume":10,"place":"Cham","citation":{"ama":"Hagengruber R. An Introduction to the Volume. In: Hagengruber RE, ed. Époque Émilienne Philosophy and Science in the Age of Émilie Du Châtelet (1706-1749). Vol 10. Women in the History of Philosophy and Science . Springer International Publishing; 2022:1-20. doi:10.1007/978-3-030-89921-9_1","ieee":"R. Hagengruber, “An Introduction to the Volume,” in Époque Émilienne Philosophy and Science in the Age of Émilie Du Châtelet (1706-1749), vol. 10, R. E. Hagengruber, Ed. Cham: Springer International Publishing, 2022, pp. 1–20.","chicago":"Hagengruber, Ruth. “An Introduction to the Volume.” In Époque Émilienne Philosophy and Science in the Age of Émilie Du Châtelet (1706-1749), edited by Ruth Edith Hagengruber, 10:1–20. Women in the History of Philosophy and Science . Cham: Springer International Publishing, 2022. https://doi.org/10.1007/978-3-030-89921-9_1.","apa":"Hagengruber, R. (2022). An Introduction to the Volume. In R. E. Hagengruber (Ed.), Époque Émilienne Philosophy and Science in the Age of Émilie Du Châtelet (1706-1749) (Vol. 10, pp. 1–20). Springer International Publishing. https://doi.org/10.1007/978-3-030-89921-9_1","short":"R. Hagengruber, in: R.E. Hagengruber (Ed.), Époque Émilienne Philosophy and Science in the Age of Émilie Du Châtelet (1706-1749), Springer International Publishing, Cham, 2022, pp. 1–20.","bibtex":"@inbook{Hagengruber_2022, place={Cham}, series={Women in the History of Philosophy and Science }, title={An Introduction to the Volume}, volume={10}, DOI={10.1007/978-3-030-89921-9_1}, booktitle={Époque Émilienne Philosophy and Science in the Age of Émilie Du Châtelet (1706-1749)}, publisher={Springer International Publishing}, author={Hagengruber, Ruth}, editor={Hagengruber, Ruth Edith}, year={2022}, pages={1–20}, collection={Women in the History of Philosophy and Science } }","mla":"Hagengruber, Ruth. “An Introduction to the Volume.” Époque Émilienne Philosophy and Science in the Age of Émilie Du Châtelet (1706-1749), edited by Ruth Edith Hagengruber, vol. 10, Springer International Publishing, 2022, pp. 1–20, doi:10.1007/978-3-030-89921-9_1."},"page":"1-20","intvolume":" 10","publication_status":"published","publication_identifier":{"isbn":["9783030899202","9783030899219"],"issn":["2523-8760","2523-8779"]},"language":[{"iso":"eng"}],"publication":"Époque Émilienne Philosophy and Science in the Age of Émilie Du Châtelet (1706-1749)","title":"An Introduction to the Volume","publisher":"Springer International Publishing","date_created":"2025-12-17T13:29:05Z","year":"2022"},{"intvolume":" 6","citation":{"mla":"Wackenrohr, Steffen, et al. “Corrosion Fatigue Behavior of Electron Beam Melted Iron in Simulated Body Fluid.” Npj Materials Degradation, vol. 6, no. 1, 18, Springer Science and Business Media LLC, 2022, doi:10.1038/s41529-022-00226-4.","bibtex":"@article{Wackenrohr_Torrent_Herbst_Nürnberger_Krooss_Ebbert_Voigt_Grundmeier_Niendorf_Maier_2022, title={Corrosion fatigue behavior of electron beam melted iron in simulated body fluid}, volume={6}, DOI={10.1038/s41529-022-00226-4}, number={118}, journal={npj Materials Degradation}, publisher={Springer Science and Business Media LLC}, author={Wackenrohr, Steffen and Torrent, Christof Johannes Jaime and Herbst, Sebastian and Nürnberger, Florian and Krooss, Philipp and Ebbert, Christoph and Voigt, Markus and Grundmeier, Guido and Niendorf, Thomas and Maier, Hans Jürgen}, year={2022} }","short":"S. Wackenrohr, C.J.J. Torrent, S. Herbst, F. Nürnberger, P. Krooss, C. Ebbert, M. Voigt, G. Grundmeier, T. Niendorf, H.J. Maier, Npj Materials Degradation 6 (2022).","apa":"Wackenrohr, S., Torrent, C. J. J., Herbst, S., Nürnberger, F., Krooss, P., Ebbert, C., Voigt, M., Grundmeier, G., Niendorf, T., & Maier, H. J. (2022). Corrosion fatigue behavior of electron beam melted iron in simulated body fluid. Npj Materials Degradation, 6(1), Article 18. https://doi.org/10.1038/s41529-022-00226-4","ama":"Wackenrohr S, Torrent CJJ, Herbst S, et al. Corrosion fatigue behavior of electron beam melted iron in simulated body fluid. npj Materials Degradation. 2022;6(1). doi:10.1038/s41529-022-00226-4","ieee":"S. Wackenrohr et al., “Corrosion fatigue behavior of electron beam melted iron in simulated body fluid,” npj Materials Degradation, vol. 6, no. 1, Art. no. 18, 2022, doi: 10.1038/s41529-022-00226-4.","chicago":"Wackenrohr, Steffen, Christof Johannes Jaime Torrent, Sebastian Herbst, Florian Nürnberger, Philipp Krooss, Christoph Ebbert, Markus Voigt, Guido Grundmeier, Thomas Niendorf, and Hans Jürgen Maier. “Corrosion Fatigue Behavior of Electron Beam Melted Iron in Simulated Body Fluid.” Npj Materials Degradation 6, no. 1 (2022). https://doi.org/10.1038/s41529-022-00226-4."},"year":"2022","issue":"1","publication_identifier":{"issn":["2397-2106"]},"publication_status":"published","doi":"10.1038/s41529-022-00226-4","title":"Corrosion fatigue behavior of electron beam melted iron in simulated body fluid","volume":6,"author":[{"last_name":"Wackenrohr","full_name":"Wackenrohr, Steffen","first_name":"Steffen"},{"first_name":"Christof Johannes Jaime","last_name":"Torrent","full_name":"Torrent, Christof Johannes Jaime"},{"first_name":"Sebastian","last_name":"Herbst","full_name":"Herbst, Sebastian"},{"first_name":"Florian","full_name":"Nürnberger, Florian","last_name":"Nürnberger"},{"first_name":"Philipp","full_name":"Krooss, Philipp","last_name":"Krooss"},{"id":"7266","full_name":"Ebbert, Christoph","last_name":"Ebbert","first_name":"Christoph"},{"last_name":"Voigt","full_name":"Voigt, Markus","id":"15182","first_name":"Markus"},{"first_name":"Guido","full_name":"Grundmeier, Guido","id":"194","last_name":"Grundmeier"},{"first_name":"Thomas","last_name":"Niendorf","full_name":"Niendorf, Thomas"},{"first_name":"Hans Jürgen","full_name":"Maier, Hans Jürgen","last_name":"Maier"}],"date_created":"2025-12-18T11:55:16Z","date_updated":"2025-12-18T11:56:57Z","publisher":"Springer Science and Business Media LLC","status":"public","abstract":[{"text":"AbstractPure iron is very attractive as a biodegradable implant material due to its high biocompatibility. In combination with additive manufacturing, which facilitates great flexibility of the implant design, it is possible to selectively adjust the microstructure of the material in the process, thereby control the corrosion and fatigue behavior. In the present study, conventional hot-rolled (HR) pure iron is compared to pure iron manufactured by electron beam melting (EBM). The microstructure, the corrosion behavior and the fatigue properties were studied comprehensively. The investigated sample conditions showed significant differences in the microstructures that led to changes in corrosion and fatigue properties. The EBM iron showed significantly lower fatigue strength compared to the HR iron. These different fatigue responses were observed under purely mechanical loading as well as with superimposed corrosion influence and are summarized in a model that describes the underlying failure mechanisms.","lang":"eng"}],"publication":"npj Materials Degradation","type":"journal_article","language":[{"iso":"eng"}],"article_number":"18","department":[{"_id":"35"},{"_id":"302"},{"_id":"321"}],"user_id":"7266","_id":"63206"},{"language":[{"iso":"eng"}],"article_number":"013701","user_id":"55629","department":[{"_id":"15"},{"_id":"230"},{"_id":"623"}],"project":[{"name":"ISOQC: Quantenkommunikation mit integrierter Optik im Zusammenhang mit supraleitender Elektronik","_id":"209"}],"_id":"33670","status":"public","type":"journal_article","publication":"Physical Review A","doi":"10.1103/physreva.106.013701","title":"Information extraction in photon-counting experiments","date_created":"2022-10-11T07:13:12Z","author":[{"first_name":"Timon","orcid":"0000-0001-7652-1716","last_name":"Schapeler","id":"55629","full_name":"Schapeler, Timon"},{"full_name":"Bartley, Tim","id":"49683","last_name":"Bartley","first_name":"Tim"}],"volume":106,"date_updated":"2025-12-18T17:07:12Z","publisher":"American Physical Society (APS)","citation":{"ama":"Schapeler T, Bartley T. Information extraction in photon-counting experiments. Physical Review A. 2022;106(1). doi:10.1103/physreva.106.013701","chicago":"Schapeler, Timon, and Tim Bartley. “Information Extraction in Photon-Counting Experiments.” Physical Review A 106, no. 1 (2022). https://doi.org/10.1103/physreva.106.013701.","ieee":"T. Schapeler and T. Bartley, “Information extraction in photon-counting experiments,” Physical Review A, vol. 106, no. 1, Art. no. 013701, 2022, doi: 10.1103/physreva.106.013701.","apa":"Schapeler, T., & Bartley, T. (2022). Information extraction in photon-counting experiments. Physical Review A, 106(1), Article 013701. https://doi.org/10.1103/physreva.106.013701","short":"T. Schapeler, T. Bartley, Physical Review A 106 (2022).","mla":"Schapeler, Timon, and Tim Bartley. “Information Extraction in Photon-Counting Experiments.” Physical Review A, vol. 106, no. 1, 013701, American Physical Society (APS), 2022, doi:10.1103/physreva.106.013701.","bibtex":"@article{Schapeler_Bartley_2022, title={Information extraction in photon-counting experiments}, volume={106}, DOI={10.1103/physreva.106.013701}, number={1013701}, journal={Physical Review A}, publisher={American Physical Society (APS)}, author={Schapeler, Timon and Bartley, Tim}, year={2022} }"},"intvolume":" 106","year":"2022","issue":"1","publication_status":"published","publication_identifier":{"issn":["2469-9926","2469-9934"]}},{"date_updated":"2025-12-18T17:37:31Z","publisher":"Elsevier BV","volume":33,"date_created":"2025-12-18T17:22:31Z","author":[{"first_name":"Jens","full_name":"Wiegmann, Jens","last_name":"Wiegmann"},{"id":"117722","full_name":"Leppin, Christian","last_name":"Leppin","first_name":"Christian"},{"first_name":"Arne","last_name":"Langhoff","full_name":"Langhoff, Arne"},{"first_name":"Jan","last_name":"Schwaderer","full_name":"Schwaderer, Jan"},{"first_name":"Sabine","last_name":"Beuermann","full_name":"Beuermann, Sabine"},{"first_name":"Diethelm","full_name":"Johannsmann, Diethelm","last_name":"Johannsmann"},{"first_name":"Alfred P.","last_name":"Weber","full_name":"Weber, Alfred P."}],"title":"Influence of the solvent evaporation rate on the β-Phase content of electrosprayed PVDF particles and films studied by a fast Multi-Overtone QCM","doi":"10.1016/j.apt.2022.103452","publication_identifier":{"issn":["0921-8831"]},"quality_controlled":"1","publication_status":"published","issue":"3","year":"2022","intvolume":" 33","citation":{"mla":"Wiegmann, Jens, et al. “Influence of the Solvent Evaporation Rate on the β-Phase Content of Electrosprayed PVDF Particles and Films Studied by a Fast Multi-Overtone QCM.” Advanced Powder Technology, vol. 33, no. 3, 103452, Elsevier BV, 2022, doi:10.1016/j.apt.2022.103452.","bibtex":"@article{Wiegmann_Leppin_Langhoff_Schwaderer_Beuermann_Johannsmann_Weber_2022, title={Influence of the solvent evaporation rate on the β-Phase content of electrosprayed PVDF particles and films studied by a fast Multi-Overtone QCM}, volume={33}, DOI={10.1016/j.apt.2022.103452}, number={3103452}, journal={Advanced Powder Technology}, publisher={Elsevier BV}, author={Wiegmann, Jens and Leppin, Christian and Langhoff, Arne and Schwaderer, Jan and Beuermann, Sabine and Johannsmann, Diethelm and Weber, Alfred P.}, year={2022} }","short":"J. Wiegmann, C. Leppin, A. Langhoff, J. Schwaderer, S. Beuermann, D. Johannsmann, A.P. Weber, Advanced Powder Technology 33 (2022).","apa":"Wiegmann, J., Leppin, C., Langhoff, A., Schwaderer, J., Beuermann, S., Johannsmann, D., & Weber, A. P. (2022). Influence of the solvent evaporation rate on the β-Phase content of electrosprayed PVDF particles and films studied by a fast Multi-Overtone QCM. Advanced Powder Technology, 33(3), Article 103452. https://doi.org/10.1016/j.apt.2022.103452","ama":"Wiegmann J, Leppin C, Langhoff A, et al. Influence of the solvent evaporation rate on the β-Phase content of electrosprayed PVDF particles and films studied by a fast Multi-Overtone QCM. Advanced Powder Technology. 2022;33(3). doi:10.1016/j.apt.2022.103452","chicago":"Wiegmann, Jens, Christian Leppin, Arne Langhoff, Jan Schwaderer, Sabine Beuermann, Diethelm Johannsmann, and Alfred P. Weber. “Influence of the Solvent Evaporation Rate on the β-Phase Content of Electrosprayed PVDF Particles and Films Studied by a Fast Multi-Overtone QCM.” Advanced Powder Technology 33, no. 3 (2022). https://doi.org/10.1016/j.apt.2022.103452.","ieee":"J. Wiegmann et al., “Influence of the solvent evaporation rate on the β-Phase content of electrosprayed PVDF particles and films studied by a fast Multi-Overtone QCM,” Advanced Powder Technology, vol. 33, no. 3, Art. no. 103452, 2022, doi: 10.1016/j.apt.2022.103452."},"_id":"63234","user_id":"117722","article_number":"103452","language":[{"iso":"eng"}],"extern":"1","publication":"Advanced Powder Technology","type":"journal_article","status":"public"},{"status":"public","type":"journal_article","extern":"1","user_id":"117722","_id":"63233","page":"10227-10233","intvolume":" 94","citation":{"bibtex":"@article{Leppin_Langhoff_Johannsmann_2022, title={Square-Wave Electrogravimetry Combined with Voltammetry Reveals Reversible Submonolayer Adsorption of Redox-Active Ions}, volume={94}, DOI={10.1021/acs.analchem.2c01763}, number={28}, journal={Analytical Chemistry}, publisher={American Chemical Society (ACS)}, author={Leppin, Christian and Langhoff, Arne and Johannsmann, Diethelm}, year={2022}, pages={10227–10233} }","mla":"Leppin, Christian, et al. “Square-Wave Electrogravimetry Combined with Voltammetry Reveals Reversible Submonolayer Adsorption of Redox-Active Ions.” Analytical Chemistry, vol. 94, no. 28, American Chemical Society (ACS), 2022, pp. 10227–33, doi:10.1021/acs.analchem.2c01763.","short":"C. Leppin, A. Langhoff, D. Johannsmann, Analytical Chemistry 94 (2022) 10227–10233.","apa":"Leppin, C., Langhoff, A., & Johannsmann, D. (2022). Square-Wave Electrogravimetry Combined with Voltammetry Reveals Reversible Submonolayer Adsorption of Redox-Active Ions. Analytical Chemistry, 94(28), 10227–10233. https://doi.org/10.1021/acs.analchem.2c01763","ama":"Leppin C, Langhoff A, Johannsmann D. Square-Wave Electrogravimetry Combined with Voltammetry Reveals Reversible Submonolayer Adsorption of Redox-Active Ions. Analytical Chemistry. 2022;94(28):10227-10233. doi:10.1021/acs.analchem.2c01763","chicago":"Leppin, Christian, Arne Langhoff, and Diethelm Johannsmann. “Square-Wave Electrogravimetry Combined with Voltammetry Reveals Reversible Submonolayer Adsorption of Redox-Active Ions.” Analytical Chemistry 94, no. 28 (2022): 10227–33. https://doi.org/10.1021/acs.analchem.2c01763.","ieee":"C. Leppin, A. Langhoff, and D. Johannsmann, “Square-Wave Electrogravimetry Combined with Voltammetry Reveals Reversible Submonolayer Adsorption of Redox-Active Ions,” Analytical Chemistry, vol. 94, no. 28, pp. 10227–10233, 2022, doi: 10.1021/acs.analchem.2c01763."},"publication_identifier":{"issn":["0003-2700","1520-6882"]},"publication_status":"published","doi":"10.1021/acs.analchem.2c01763","volume":94,"author":[{"first_name":"Christian","last_name":"Leppin","full_name":"Leppin, Christian","id":"117722"},{"last_name":"Langhoff","full_name":"Langhoff, Arne","first_name":"Arne"},{"last_name":"Johannsmann","full_name":"Johannsmann, Diethelm","first_name":"Diethelm"}],"date_updated":"2025-12-18T17:38:07Z","publication":"Analytical Chemistry","language":[{"iso":"eng"}],"year":"2022","issue":"28","quality_controlled":"1","title":"Square-Wave Electrogravimetry Combined with Voltammetry Reveals Reversible Submonolayer Adsorption of Redox-Active Ions","date_created":"2025-12-18T17:21:21Z","publisher":"American Chemical Society (ACS)"},{"type":"journal_article","publication":"Advanced Nonlinear Studies","abstract":[{"lang":"eng","text":"AbstractThe chemotaxis–Stokes systemnt+u⋅∇n=∇⋅(D(n)∇n)−∇⋅(nS(x,n,c)⋅∇c),ct+u⋅∇c=Δc−nc,ut=Δu+∇P+n∇Φ,∇⋅u=0,\\left\\{\\begin{array}{l}{n}_{t}+u\\cdot \\nabla n=\\nabla \\cdot (D\\left(n)\\nabla n)-\\nabla \\cdot (nS\\left(x,n,c)\\cdot \\nabla c),\\\\ {c}_{t}+u\\cdot \\nabla c=\\Delta c-nc,\\\\ {u}_{t}=\\Delta u+\\nabla P+n\\nabla \\Phi ,\\hspace{1.0em}\\nabla \\cdot u=0,\\end{array}\\right.is considered in a smoothly bounded convex domainΩ⊂R3\\Omega \\subset {{\\mathbb{R}}}^{3}, with given suitably regular functionsD:[0,∞)→[0,∞)D:{[}0,\\infty )\\to {[}0,\\infty ),S:Ω¯×[0,∞)×(0,∞)→R3×3S:\\overline{\\Omega }\\times {[}0,\\infty )\\times \\left(0,\\infty )\\to {{\\mathbb{R}}}^{3\\times 3}andΦ:Ω¯→R\\Phi :\\overline{\\Omega }\\to {\\mathbb{R}}such thatD>0D\\gt 0on(0,∞)\\left(0,\\infty ). It is shown that if with some nondecreasingS0:(0,∞)→(0,∞){S}_{0}:\\left(0,\\infty )\\to \\left(0,\\infty )we have∣S(x,n,c)∣≤S0(c)c12for all(x,n,c)∈Ω¯×[0,∞)×(0,∞),| S\\left(x,n,c)| \\le \\frac{{S}_{0}\\left(c)}{{c}^{\\tfrac{1}{2}}}\\hspace{1.0em}\\hspace{0.1em}\\text{for all}\\hspace{0.1em}\\hspace{0.33em}\\left(x,n,c)\\in \\overline{\\Omega }\\times {[}0,\\infty )\\times \\left(0,\\infty ),then for allM>0M\\gt 0there existsL(M)>0L\\left(M)\\gt 0such that wheneverliminfn→∞D(n)>L(M)andliminfn↘0D(n)n>0,\\mathop{\\mathrm{liminf}}\\limits_{n\\to \\infty }D\\left(n)\\gt L\\left(M)\\hspace{1.0em}\\hspace{0.1em}\\text{and}\\hspace{0.1em}\\hspace{1.0em}\\mathop{\\mathrm{liminf}}\\limits_{n\\searrow 0}\\frac{D\\left(n)}{n}\\gt 0,for all sufficiently regular initial data(n0,c0,u0)\\left({n}_{0},{c}_{0},{u}_{0})fulfilling‖c0‖L∞(Ω)≤M\\Vert {c}_{0}{\\Vert }_{{L}^{\\infty }\\left(\\Omega )}\\le Man associated no-flux/no-flux/Dirichlet initial-boundary value problem admits a global bounded weak solution, classical if additionallyD(0)>0D\\left(0)\\gt 0. When combined with previously known results, this particularly implies global existence of bounded solutions whenD(n)=nm−1D\\left(n)={n}^{m-1},n≥0n\\ge 0, with arbitrarym>1m\\gt 1, but beyond this asserts global boundedness also in the presence of diffusivities which exhibit arbitrarily slow divergence to+∞+\\inftyat large densities and of possibly singular chemotactic sensitivities."}],"status":"public","_id":"63310","user_id":"31496","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["2169-0375"]},"issue":"1","year":"2022","citation":{"ama":"Winkler M. Chemotaxis-Stokes interaction with very weak diffusion enhancement: Blow-up exclusion via detection of absorption-induced entropy structures involving multiplicative couplings. Advanced Nonlinear Studies. 2022;22(1):88-117. doi:10.1515/ans-2022-0004","chicago":"Winkler, Michael. “Chemotaxis-Stokes Interaction with Very Weak Diffusion Enhancement: Blow-up Exclusion via Detection of Absorption-Induced Entropy Structures Involving Multiplicative Couplings.” Advanced Nonlinear Studies 22, no. 1 (2022): 88–117. https://doi.org/10.1515/ans-2022-0004.","ieee":"M. Winkler, “Chemotaxis-Stokes interaction with very weak diffusion enhancement: Blow-up exclusion via detection of absorption-induced entropy structures involving multiplicative couplings,” Advanced Nonlinear Studies, vol. 22, no. 1, pp. 88–117, 2022, doi: 10.1515/ans-2022-0004.","short":"M. Winkler, Advanced Nonlinear Studies 22 (2022) 88–117.","bibtex":"@article{Winkler_2022, title={Chemotaxis-Stokes interaction with very weak diffusion enhancement: Blow-up exclusion via detection of absorption-induced entropy structures involving multiplicative couplings}, volume={22}, DOI={10.1515/ans-2022-0004}, number={1}, journal={Advanced Nonlinear Studies}, publisher={Walter de Gruyter GmbH}, author={Winkler, Michael}, year={2022}, pages={88–117} }","mla":"Winkler, Michael. “Chemotaxis-Stokes Interaction with Very Weak Diffusion Enhancement: Blow-up Exclusion via Detection of Absorption-Induced Entropy Structures Involving Multiplicative Couplings.” Advanced Nonlinear Studies, vol. 22, no. 1, Walter de Gruyter GmbH, 2022, pp. 88–117, doi:10.1515/ans-2022-0004.","apa":"Winkler, M. (2022). Chemotaxis-Stokes interaction with very weak diffusion enhancement: Blow-up exclusion via detection of absorption-induced entropy structures involving multiplicative couplings. Advanced Nonlinear Studies, 22(1), 88–117. https://doi.org/10.1515/ans-2022-0004"},"intvolume":" 22","page":"88-117","publisher":"Walter de Gruyter GmbH","date_updated":"2025-12-18T20:05:30Z","author":[{"last_name":"Winkler","id":"31496","full_name":"Winkler, Michael","first_name":"Michael"}],"date_created":"2025-12-18T19:29:40Z","volume":22,"title":"Chemotaxis-Stokes interaction with very weak diffusion enhancement: Blow-up exclusion via detection of absorption-induced entropy structures involving multiplicative couplings","doi":"10.1515/ans-2022-0004"},{"article_number":"108","language":[{"iso":"eng"}],"_id":"63305","user_id":"31496","abstract":[{"text":"AbstractA no-flux initial-boundary value problem for the doubly degenrate parabolic system $$\\begin{aligned} \\left\\{ \\begin{array}{l} u_t = \\nabla \\cdot \\big ( uv\\nabla u\\big ) + \\ell uv, \\\\ v_t = \\Delta v - uv, \\end{array} \\right. \\qquad \\qquad (\\star ) \\end{aligned}$$\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n u\r\n t\r\n \r\n =\r\n ∇\r\n ·\r\n \r\n (\r\n \r\n u\r\n v\r\n ∇\r\n u\r\n \r\n )\r\n \r\n +\r\n ℓ\r\n u\r\n v\r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n v\r\n t\r\n \r\n =\r\n Δ\r\n v\r\n -\r\n u\r\n v\r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n (\r\n ⋆\r\n )\r\n \r\n \r\n \r\n \r\n \r\n \r\n is considered in a smoothly bounded convex domain $$\\Omega \\subset \\mathbb {R}^n$$\r\n \r\n Ω\r\n ⊂\r\n \r\n \r\n R\r\n \r\n n\r\n \r\n \r\n , with $$n\\ge 1$$\r\n \r\n n\r\n ≥\r\n 1\r\n \r\n and $$\\ell \\ge 0$$\r\n \r\n ℓ\r\n ≥\r\n 0\r\n \r\n . The first of the main results asserts that for nonnegative initial data $$(u_0,v_0)\\in (L^\\infty (\\Omega ))^2$$\r\n \r\n \r\n (\r\n \r\n u\r\n 0\r\n \r\n ,\r\n \r\n v\r\n 0\r\n \r\n )\r\n \r\n ∈\r\n \r\n \r\n (\r\n \r\n L\r\n ∞\r\n \r\n \r\n (\r\n Ω\r\n )\r\n \r\n )\r\n \r\n 2\r\n \r\n \r\n with $$u_0\\not \\equiv 0$$\r\n \r\n \r\n u\r\n 0\r\n \r\n ≢\r\n 0\r\n \r\n , $$v_0\\not \\equiv 0$$\r\n \r\n \r\n v\r\n 0\r\n \r\n ≢\r\n 0\r\n \r\n and $$\\sqrt{v_0}\\in W^{1,2}(\\Omega )$$\r\n \r\n \r\n \r\n v\r\n 0\r\n \r\n \r\n ∈\r\n \r\n W\r\n \r\n 1\r\n ,\r\n 2\r\n \r\n \r\n \r\n (\r\n Ω\r\n )\r\n \r\n \r\n , there exists a global weak solution (u, v) which, inter alia, belongs to $$C^0(\\overline{\\Omega }\\times (0,\\infty )) \\times C^{2,1}(\\overline{\\Omega }\\times (0,\\infty ))$$\r\n \r\n \r\n C\r\n 0\r\n \r\n \r\n (\r\n \r\n Ω\r\n ¯\r\n \r\n ×\r\n \r\n (\r\n 0\r\n ,\r\n ∞\r\n )\r\n \r\n )\r\n \r\n ×\r\n \r\n C\r\n \r\n 2\r\n ,\r\n 1\r\n \r\n \r\n \r\n (\r\n \r\n Ω\r\n ¯\r\n \r\n ×\r\n \r\n (\r\n 0\r\n ,\r\n ∞\r\n )\r\n \r\n )\r\n \r\n \r\n and satisfies $$\\sup _{t>0} \\Vert u(\\cdot ,t)\\Vert _{L^p(\\Omega )}<\\infty $$\r\n \r\n \r\n sup\r\n \r\n t\r\n >\r\n 0\r\n \r\n \r\n \r\n \r\n ‖\r\n u\r\n \r\n (\r\n ·\r\n ,\r\n t\r\n )\r\n \r\n ‖\r\n \r\n \r\n \r\n L\r\n p\r\n \r\n \r\n (\r\n Ω\r\n )\r\n \r\n \r\n \r\n <\r\n ∞\r\n \r\n for all $$p\\in [1,p_0)$$\r\n \r\n p\r\n ∈\r\n [\r\n 1\r\n ,\r\n \r\n p\r\n 0\r\n \r\n )\r\n \r\n with $$p_0:=\\frac{n}{(n-2)_+}$$\r\n \r\n \r\n p\r\n 0\r\n \r\n :\r\n =\r\n \r\n n\r\n \r\n \r\n (\r\n n\r\n -\r\n 2\r\n )\r\n \r\n +\r\n \r\n \r\n \r\n . It is next seen that for each of these solutions one can find $$u_\\infty \\in \\bigcap _{p\\in [1,p_0)} L^p(\\Omega )$$\r\n \r\n \r\n u\r\n ∞\r\n \r\n ∈\r\n \r\n ⋂\r\n \r\n p\r\n ∈\r\n [\r\n 1\r\n ,\r\n \r\n p\r\n 0\r\n \r\n )\r\n \r\n \r\n \r\n L\r\n p\r\n \r\n \r\n (\r\n Ω\r\n )\r\n \r\n \r\n such that, within an appropriate topological setting, $$(u(\\cdot ,t),v(\\cdot ,t))$$\r\n \r\n (\r\n u\r\n (\r\n ·\r\n ,\r\n t\r\n )\r\n ,\r\n v\r\n (\r\n ·\r\n ,\r\n t\r\n )\r\n )\r\n \r\n approaches the equilibrium $$(u_\\infty ,0)$$\r\n \r\n (\r\n \r\n u\r\n ∞\r\n \r\n ,\r\n 0\r\n )\r\n \r\n in the large time limit. Finally, in the case $$n\\le 5$$\r\n \r\n n\r\n ≤\r\n 5\r\n \r\n a result ensuring a certain stability property of any member in the uncountably large family of steady states $$(u_0,0)$$\r\n \r\n (\r\n \r\n u\r\n 0\r\n \r\n ,\r\n 0\r\n )\r\n \r\n , with arbitrary and suitably regular $$u_0:\\Omega \\rightarrow [0,\\infty )$$\r\n \r\n \r\n u\r\n 0\r\n \r\n :\r\n Ω\r\n →\r\n \r\n [\r\n 0\r\n ,\r\n ∞\r\n )\r\n \r\n \r\n , is derived. This provides some rigorous evidence for the appropriateness of ($$\\star $$\r\n ⋆\r\n ) to model the emergence of a strikingly large variety of stable structures observed in experiments on bacterial motion in nutrient-poor environments. Essential parts of the analysis rely on the use of an apparently novel class of functional inequalities to suitably cope with the doubly degenerate diffusion mechanism in ($$\\star $$\r\n ⋆\r\n ).","lang":"eng"}],"status":"public","publication":"Calculus of Variations and Partial Differential Equations","type":"journal_article","title":"Stabilization of arbitrary structures in a doubly degenerate reaction-diffusion system modeling bacterial motion on a nutrient-poor agar","doi":"10.1007/s00526-021-02168-2","date_updated":"2025-12-18T20:04:43Z","publisher":"Springer Science and Business Media LLC","volume":61,"date_created":"2025-12-18T19:26:32Z","author":[{"first_name":"Michael","last_name":"Winkler","id":"31496","full_name":"Winkler, Michael"}],"year":"2022","intvolume":" 61","citation":{"ama":"Winkler M. Stabilization of arbitrary structures in a doubly degenerate reaction-diffusion system modeling bacterial motion on a nutrient-poor agar. Calculus of Variations and Partial Differential Equations. 2022;61(3). doi:10.1007/s00526-021-02168-2","chicago":"Winkler, Michael. “Stabilization of Arbitrary Structures in a Doubly Degenerate Reaction-Diffusion System Modeling Bacterial Motion on a Nutrient-Poor Agar.” Calculus of Variations and Partial Differential Equations 61, no. 3 (2022). https://doi.org/10.1007/s00526-021-02168-2.","ieee":"M. Winkler, “Stabilization of arbitrary structures in a doubly degenerate reaction-diffusion system modeling bacterial motion on a nutrient-poor agar,” Calculus of Variations and Partial Differential Equations, vol. 61, no. 3, Art. no. 108, 2022, doi: 10.1007/s00526-021-02168-2.","short":"M. Winkler, Calculus of Variations and Partial Differential Equations 61 (2022).","mla":"Winkler, Michael. “Stabilization of Arbitrary Structures in a Doubly Degenerate Reaction-Diffusion System Modeling Bacterial Motion on a Nutrient-Poor Agar.” Calculus of Variations and Partial Differential Equations, vol. 61, no. 3, 108, Springer Science and Business Media LLC, 2022, doi:10.1007/s00526-021-02168-2.","bibtex":"@article{Winkler_2022, title={Stabilization of arbitrary structures in a doubly degenerate reaction-diffusion system modeling bacterial motion on a nutrient-poor agar}, volume={61}, DOI={10.1007/s00526-021-02168-2}, number={3108}, journal={Calculus of Variations and Partial Differential Equations}, publisher={Springer Science and Business Media LLC}, author={Winkler, Michael}, year={2022} }","apa":"Winkler, M. (2022). Stabilization of arbitrary structures in a doubly degenerate reaction-diffusion system modeling bacterial motion on a nutrient-poor agar. Calculus of Variations and Partial Differential Equations, 61(3), Article 108. https://doi.org/10.1007/s00526-021-02168-2"},"publication_identifier":{"issn":["0944-2669","1432-0835"]},"publication_status":"published","issue":"3"},{"status":"public","abstract":[{"text":"AbstractThe Cauchy problem in $$\\mathbb {R}^n$$\r\n \r\n \r\n R\r\n \r\n n\r\n \r\n , $$n\\ge 1$$\r\n \r\n n\r\n ≥\r\n 1\r\n \r\n , for the degenerate parabolic equation $$\\begin{aligned} u_t=u^p \\Delta u \\qquad \\qquad (\\star ) \\end{aligned}$$\r\n \r\n \r\n \r\n \r\n \r\n \r\n u\r\n t\r\n \r\n =\r\n \r\n u\r\n p\r\n \r\n Δ\r\n u\r\n \r\n \r\n \r\n (\r\n ⋆\r\n )\r\n \r\n \r\n \r\n \r\n \r\n \r\n is considered for $$p\\ge 1$$\r\n \r\n p\r\n ≥\r\n 1\r\n \r\n . It is shown that given any positive $$f\\in C^0([0,\\infty ))$$\r\n \r\n f\r\n ∈\r\n \r\n C\r\n 0\r\n \r\n \r\n (\r\n \r\n [\r\n 0\r\n ,\r\n ∞\r\n )\r\n \r\n )\r\n \r\n \r\n and $$g\\in C^0([0,\\infty ))$$\r\n \r\n g\r\n ∈\r\n \r\n C\r\n 0\r\n \r\n \r\n (\r\n \r\n [\r\n 0\r\n ,\r\n ∞\r\n )\r\n \r\n )\r\n \r\n \r\n satisfying $$\\begin{aligned} f(t)\\rightarrow + \\infty \\quad \\text{ and } \\quad g(t)\\rightarrow 0 \\qquad \\text{ as } t\\rightarrow \\infty , \\end{aligned}$$\r\n \r\n \r\n \r\n \r\n \r\n f\r\n (\r\n t\r\n )\r\n →\r\n +\r\n ∞\r\n \r\n \r\n and\r\n \r\n \r\n g\r\n (\r\n t\r\n )\r\n →\r\n 0\r\n \r\n \r\n as\r\n \r\n t\r\n →\r\n ∞\r\n ,\r\n \r\n \r\n \r\n \r\n \r\n one can find positive and radially symmetric continuous initial data with the property that the initial value problem for ($$\\star $$\r\n ⋆\r\n ) admits a positive classical solution such that $$\\begin{aligned} t^\\frac{1}{p} \\Vert u(\\cdot ,t)\\Vert _{L^\\infty (\\mathbb {R}^n)} \\rightarrow \\infty \\qquad \\text{ and } \\qquad \\Vert u(\\cdot ,t)\\Vert _{L^\\infty (\\mathbb {R}^n)} \\rightarrow 0 \\qquad \\text{ as } t\\rightarrow \\infty , \\end{aligned}$$\r\n \r\n \r\n \r\n \r\n \r\n \r\n t\r\n \r\n 1\r\n p\r\n \r\n \r\n \r\n \r\n ‖\r\n u\r\n \r\n (\r\n ·\r\n ,\r\n t\r\n )\r\n \r\n ‖\r\n \r\n \r\n \r\n L\r\n ∞\r\n \r\n \r\n (\r\n \r\n \r\n R\r\n \r\n n\r\n \r\n )\r\n \r\n \r\n \r\n →\r\n ∞\r\n \r\n \r\n and\r\n \r\n \r\n \r\n \r\n ‖\r\n u\r\n \r\n (\r\n ·\r\n ,\r\n t\r\n )\r\n \r\n ‖\r\n \r\n \r\n \r\n L\r\n ∞\r\n \r\n \r\n (\r\n \r\n \r\n R\r\n \r\n n\r\n \r\n )\r\n \r\n \r\n \r\n →\r\n 0\r\n \r\n \r\n as\r\n \r\n t\r\n →\r\n ∞\r\n ,\r\n \r\n \r\n \r\n \r\n \r\n but that $$\\begin{aligned} \\liminf _{t\\rightarrow \\infty } \\frac{t^\\frac{1}{p} \\Vert u(\\cdot ,t)\\Vert _{L^\\infty (\\mathbb {R}^n)}}{f(t)} =0 \\end{aligned}$$\r\n \r\n \r\n \r\n \r\n \r\n \r\n lim inf\r\n \r\n t\r\n →\r\n ∞\r\n \r\n \r\n \r\n \r\n \r\n t\r\n \r\n 1\r\n p\r\n \r\n \r\n \r\n \r\n ‖\r\n u\r\n \r\n (\r\n ·\r\n ,\r\n t\r\n )\r\n \r\n ‖\r\n \r\n \r\n \r\n L\r\n ∞\r\n \r\n \r\n (\r\n \r\n \r\n R\r\n \r\n n\r\n \r\n )\r\n \r\n \r\n \r\n \r\n \r\n f\r\n (\r\n t\r\n )\r\n \r\n \r\n =\r\n 0\r\n \r\n \r\n \r\n \r\n \r\n and $$\\begin{aligned} \\limsup _{t\\rightarrow \\infty } \\frac{\\Vert u(\\cdot ,t)\\Vert _{L^\\infty (\\mathbb {R}^n)}}{g(t)} =\\infty . \\end{aligned}$$\r\n \r\n \r\n \r\n \r\n \r\n \r\n lim sup\r\n \r\n t\r\n →\r\n ∞\r\n \r\n \r\n \r\n \r\n \r\n ‖\r\n u\r\n \r\n (\r\n ·\r\n ,\r\n t\r\n )\r\n \r\n ‖\r\n \r\n \r\n \r\n L\r\n ∞\r\n \r\n \r\n (\r\n \r\n \r\n R\r\n \r\n n\r\n \r\n )\r\n \r\n \r\n \r\n \r\n g\r\n (\r\n t\r\n )\r\n \r\n \r\n =\r\n ∞\r\n .\r\n \r\n \r\n \r\n \r\n \r\n ","lang":"eng"}],"type":"journal_article","publication":"Partial Differential Equations and Applications","language":[{"iso":"eng"}],"article_number":"47","user_id":"31496","_id":"63311","citation":{"bibtex":"@article{Winkler_2022, title={Oscillatory decay in a degenerate parabolic equation}, volume={3}, DOI={10.1007/s42985-022-00186-z}, number={447}, journal={Partial Differential Equations and Applications}, publisher={Springer Science and Business Media LLC}, author={Winkler, Michael}, year={2022} }","short":"M. Winkler, Partial Differential Equations and Applications 3 (2022).","mla":"Winkler, Michael. “Oscillatory Decay in a Degenerate Parabolic Equation.” Partial Differential Equations and Applications, vol. 3, no. 4, 47, Springer Science and Business Media LLC, 2022, doi:10.1007/s42985-022-00186-z.","apa":"Winkler, M. (2022). Oscillatory decay in a degenerate parabolic equation. Partial Differential Equations and Applications, 3(4), Article 47. https://doi.org/10.1007/s42985-022-00186-z","ama":"Winkler M. Oscillatory decay in a degenerate parabolic equation. Partial Differential Equations and Applications. 2022;3(4). doi:10.1007/s42985-022-00186-z","ieee":"M. Winkler, “Oscillatory decay in a degenerate parabolic equation,” Partial Differential Equations and Applications, vol. 3, no. 4, Art. no. 47, 2022, doi: 10.1007/s42985-022-00186-z.","chicago":"Winkler, Michael. “Oscillatory Decay in a Degenerate Parabolic Equation.” Partial Differential Equations and Applications 3, no. 4 (2022). https://doi.org/10.1007/s42985-022-00186-z."},"intvolume":" 3","year":"2022","issue":"4","publication_status":"published","publication_identifier":{"issn":["2662-2963","2662-2971"]},"doi":"10.1007/s42985-022-00186-z","title":"Oscillatory decay in a degenerate parabolic equation","author":[{"first_name":"Michael","id":"31496","full_name":"Winkler, Michael","last_name":"Winkler"}],"date_created":"2025-12-18T19:30:04Z","volume":3,"publisher":"Springer Science and Business Media LLC","date_updated":"2025-12-18T20:05:38Z"},{"publication_status":"published","publication_identifier":{"issn":["1531-3492","1553-524X"]},"issue":"11","year":"2022","citation":{"apa":"Winkler, M. (2022). Approaching logarithmic singularities in quasilinear chemotaxis-consumption systems with signal-dependent sensitivities. Discrete and Continuous Dynamical Systems - B, 27(11), Article 6565. https://doi.org/10.3934/dcdsb.2022009","short":"M. Winkler, Discrete and Continuous Dynamical Systems - B 27 (2022).","mla":"Winkler, Michael. “Approaching Logarithmic Singularities in Quasilinear Chemotaxis-Consumption Systems with Signal-Dependent Sensitivities.” Discrete and Continuous Dynamical Systems - B, vol. 27, no. 11, 6565, American Institute of Mathematical Sciences (AIMS), 2022, doi:10.3934/dcdsb.2022009.","bibtex":"@article{Winkler_2022, title={Approaching logarithmic singularities in quasilinear chemotaxis-consumption systems with signal-dependent sensitivities}, volume={27}, DOI={10.3934/dcdsb.2022009}, number={116565}, journal={Discrete and Continuous Dynamical Systems - B}, publisher={American Institute of Mathematical Sciences (AIMS)}, author={Winkler, Michael}, year={2022} }","ama":"Winkler M. Approaching logarithmic singularities in quasilinear chemotaxis-consumption systems with signal-dependent sensitivities. Discrete and Continuous Dynamical Systems - B. 2022;27(11). doi:10.3934/dcdsb.2022009","ieee":"M. Winkler, “Approaching logarithmic singularities in quasilinear chemotaxis-consumption systems with signal-dependent sensitivities,” Discrete and Continuous Dynamical Systems - B, vol. 27, no. 11, Art. no. 6565, 2022, doi: 10.3934/dcdsb.2022009.","chicago":"Winkler, Michael. “Approaching Logarithmic Singularities in Quasilinear Chemotaxis-Consumption Systems with Signal-Dependent Sensitivities.” Discrete and Continuous Dynamical Systems - B 27, no. 11 (2022). https://doi.org/10.3934/dcdsb.2022009."},"intvolume":" 27","date_updated":"2025-12-18T20:05:47Z","publisher":"American Institute of Mathematical Sciences (AIMS)","date_created":"2025-12-18T19:30:32Z","author":[{"first_name":"Michael","last_name":"Winkler","id":"31496","full_name":"Winkler, Michael"}],"volume":27,"title":"Approaching logarithmic singularities in quasilinear chemotaxis-consumption systems with signal-dependent sensitivities","doi":"10.3934/dcdsb.2022009","type":"journal_article","publication":"Discrete and Continuous Dynamical Systems - B","abstract":[{"text":"<p style='text-indent:20px;'>The chemotaxis system</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id=\"FE1\"> \\begin{document}$ \\begin{array}{l}\\left\\{ \\begin{array}{l} \tu_t = \\nabla \\cdot \\big( D(u) \\nabla u \\big) - \\nabla \\cdot \\big( uS(x, u, v)\\cdot \\nabla v\\big), \\\\ \tv_t = \\Delta v -uv, \\end{array} \\right. \\end{array} $\\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>is considered in a bounded domain <inline-formula><tex-math id=\"M1\">\\begin{document}$ \\Omega\\subset \\mathbb{R}^n $\\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id=\"M2\">\\begin{document}$ n\\ge 2 $\\end{document}</tex-math></inline-formula>, with smooth boundary.</p><p style='text-indent:20px;'>It is shown that if <inline-formula><tex-math id=\"M3\">\\begin{document}$ D: [0, \\infty) \\to [0, \\infty) $\\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id=\"M4\">\\begin{document}$ S: \\overline{\\Omega}\\times [0, \\infty)\\times (0, \\infty)\\to \\mathbb{R}^{n\\times n} $\\end{document}</tex-math></inline-formula> are suitably smooth functions satisfying</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id=\"FE2\"> \\begin{document}$ \\begin{array}{l}D(u) \\ge k_D u^{m-1} \t\\qquad {\\rm{for\\; all}}\\; u\\ge 0 \\end{array} $\\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>and</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id=\"FE3\"> \\begin{document}$ \\begin{array}{l}|S(x, u, v)| \\le \\frac{S_0(v)}{v^\\alpha} \\qquad {\\rm{for\\; all}}\\; (x, u, v)\\; \\in \\Omega\\times (0, \\infty)^2 \\end{array} $\\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>with some</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id=\"FE4\"> \\begin{document}$ \\begin{array}{l}m&gt;\\frac{3n-2}{2n} \t\\qquad {\\rm{and}}\\;\\alpha\\in [0, 1), \\end{array} $\\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>and with some <inline-formula><tex-math id=\"M5\">\\begin{document}$ k_D&gt;0 $\\end{document}</tex-math></inline-formula> and nondecreasing <inline-formula><tex-math id=\"M6\">\\begin{document}$ S_0: (0, \\infty)\\to (0, \\infty) $\\end{document}</tex-math></inline-formula>, then for all suitably regular initial data a corresponding no-flux type initial-boundary value problem admits a global bounded weak solution which actually is smooth and classical if <inline-formula><tex-math id=\"M7\">\\begin{document}$ D(0)&gt;0 $\\end{document}</tex-math></inline-formula>.</p>","lang":"eng"}],"status":"public","_id":"63312","user_id":"31496","article_number":"6565","language":[{"iso":"eng"}]},{"status":"public","abstract":[{"lang":"eng","text":"AbstractThis manuscript is concerned with the problem of efficiently estimating chemotactic gradients, as forming a ubiquitous issue of key importance in virtually any proof of boundedness features in Keller–Segel type systems. A strategy is proposed which at its core relies on bounds for such quantities, conditional in the sense of involving certain Lebesgue norms of solution components that explicitly influence the signal evolution.Applications of this procedure firstly provide apparently novel boundedness results for two particular classes chemotaxis systems, and apart from that are shown to significantly condense proofs for basically well‐known statements on boundedness in two further Keller–Segel type problems."}],"publication":"Mathematische Nachrichten","type":"journal_article","language":[{"iso":"eng"}],"user_id":"31496","_id":"63309","intvolume":" 295","page":"1840-1862","citation":{"apa":"Winkler, M. (2022). A unifying approach toward boundedness in Keller–Segel type cross‐diffusion systems via conditional L∞$L^\\infty$ estimates for taxis gradients. Mathematische Nachrichten, 295(9), 1840–1862. https://doi.org/10.1002/mana.202000403","short":"M. Winkler, Mathematische Nachrichten 295 (2022) 1840–1862.","mla":"Winkler, Michael. “A Unifying Approach toward Boundedness in Keller–Segel Type Cross‐diffusion Systems via Conditional L∞$L^\\infty$ Estimates for Taxis Gradients.” Mathematische Nachrichten, vol. 295, no. 9, Wiley, 2022, pp. 1840–62, doi:10.1002/mana.202000403.","bibtex":"@article{Winkler_2022, title={A unifying approach toward boundedness in Keller–Segel type cross‐diffusion systems via conditional L∞$L^\\infty$ estimates for taxis gradients}, volume={295}, DOI={10.1002/mana.202000403}, number={9}, journal={Mathematische Nachrichten}, publisher={Wiley}, author={Winkler, Michael}, year={2022}, pages={1840–1862} }","chicago":"Winkler, Michael. “A Unifying Approach toward Boundedness in Keller–Segel Type Cross‐diffusion Systems via Conditional L∞$L^\\infty$ Estimates for Taxis Gradients.” Mathematische Nachrichten 295, no. 9 (2022): 1840–62. https://doi.org/10.1002/mana.202000403.","ieee":"M. Winkler, “A unifying approach toward boundedness in Keller–Segel type cross‐diffusion systems via conditional L∞$L^\\infty$ estimates for taxis gradients,” Mathematische Nachrichten, vol. 295, no. 9, pp. 1840–1862, 2022, doi: 10.1002/mana.202000403.","ama":"Winkler M. A unifying approach toward boundedness in Keller–Segel type cross‐diffusion systems via conditional L∞$L^\\infty$ estimates for taxis gradients. Mathematische Nachrichten. 2022;295(9):1840-1862. doi:10.1002/mana.202000403"},"year":"2022","issue":"9","publication_identifier":{"issn":["0025-584X","1522-2616"]},"publication_status":"published","doi":"10.1002/mana.202000403","title":"A unifying approach toward boundedness in Keller–Segel type cross‐diffusion systems via conditional L∞$L^\\infty$ estimates for taxis gradients","volume":295,"author":[{"last_name":"Winkler","id":"31496","full_name":"Winkler, Michael","first_name":"Michael"}],"date_created":"2025-12-18T19:28:46Z","date_updated":"2025-12-18T20:05:19Z","publisher":"Wiley"},{"doi":"10.1512/iumj.2022.71.9042","title":"A critical blow-up exponent for flux limiation in a Keller-Segel system","volume":71,"author":[{"first_name":"Michael","last_name":"Winkler","full_name":"Winkler, Michael","id":"31496"}],"date_created":"2025-12-18T19:26:56Z","publisher":"Indiana University Mathematics Journal","date_updated":"2025-12-18T20:04:53Z","intvolume":" 71","page":"1437-1465","citation":{"chicago":"Winkler, Michael. “A Critical Blow-up Exponent for Flux Limiation in a Keller-Segel System.” Indiana University Mathematics Journal 71, no. 4 (2022): 1437–65. https://doi.org/10.1512/iumj.2022.71.9042.","ieee":"M. Winkler, “A critical blow-up exponent for flux limiation in a Keller-Segel system,” Indiana University Mathematics Journal, vol. 71, no. 4, pp. 1437–1465, 2022, doi: 10.1512/iumj.2022.71.9042.","ama":"Winkler M. A critical blow-up exponent for flux limiation in a Keller-Segel system. Indiana University Mathematics Journal. 2022;71(4):1437-1465. doi:10.1512/iumj.2022.71.9042","apa":"Winkler, M. (2022). A critical blow-up exponent for flux limiation in a Keller-Segel system. Indiana University Mathematics Journal, 71(4), 1437–1465. https://doi.org/10.1512/iumj.2022.71.9042","bibtex":"@article{Winkler_2022, title={A critical blow-up exponent for flux limiation in a Keller-Segel system}, volume={71}, DOI={10.1512/iumj.2022.71.9042}, number={4}, journal={Indiana University Mathematics Journal}, publisher={Indiana University Mathematics Journal}, author={Winkler, Michael}, year={2022}, pages={1437–1465} }","mla":"Winkler, Michael. “A Critical Blow-up Exponent for Flux Limiation in a Keller-Segel System.” Indiana University Mathematics Journal, vol. 71, no. 4, Indiana University Mathematics Journal, 2022, pp. 1437–65, doi:10.1512/iumj.2022.71.9042.","short":"M. Winkler, Indiana University Mathematics Journal 71 (2022) 1437–1465."},"year":"2022","issue":"4","publication_identifier":{"issn":["0022-2518"]},"publication_status":"published","language":[{"iso":"eng"}],"user_id":"31496","_id":"63306","status":"public","publication":"Indiana University Mathematics Journal","type":"journal_article"},{"publication_status":"published","publication_identifier":{"issn":["1664-3607","1664-3615"]},"issue":"02","year":"2022","citation":{"apa":"Winkler, M. (2022). Application of the Moser–Trudinger inequality in the construction of global solutions to a strongly degenerate migration model. Bulletin of Mathematical Sciences, 13(02), Article 2250012. https://doi.org/10.1142/s1664360722500126","short":"M. Winkler, Bulletin of Mathematical Sciences 13 (2022).","bibtex":"@article{Winkler_2022, title={Application of the Moser–Trudinger inequality in the construction of global solutions to a strongly degenerate migration model}, volume={13}, DOI={10.1142/s1664360722500126}, number={022250012}, journal={Bulletin of Mathematical Sciences}, publisher={World Scientific Pub Co Pte Ltd}, author={Winkler, Michael}, year={2022} }","mla":"Winkler, Michael. “Application of the Moser–Trudinger Inequality in the Construction of Global Solutions to a Strongly Degenerate Migration Model.” Bulletin of Mathematical Sciences, vol. 13, no. 02, 2250012, World Scientific Pub Co Pte Ltd, 2022, doi:10.1142/s1664360722500126.","ieee":"M. Winkler, “Application of the Moser–Trudinger inequality in the construction of global solutions to a strongly degenerate migration model,” Bulletin of Mathematical Sciences, vol. 13, no. 02, Art. no. 2250012, 2022, doi: 10.1142/s1664360722500126.","chicago":"Winkler, Michael. “Application of the Moser–Trudinger Inequality in the Construction of Global Solutions to a Strongly Degenerate Migration Model.” Bulletin of Mathematical Sciences 13, no. 02 (2022). https://doi.org/10.1142/s1664360722500126.","ama":"Winkler M. Application of the Moser–Trudinger inequality in the construction of global solutions to a strongly degenerate migration model. Bulletin of Mathematical Sciences. 2022;13(02). doi:10.1142/s1664360722500126"},"intvolume":" 13","date_updated":"2025-12-18T20:07:05Z","publisher":"World Scientific Pub Co Pte Ltd","author":[{"full_name":"Winkler, Michael","id":"31496","last_name":"Winkler","first_name":"Michael"}],"date_created":"2025-12-18T19:18:11Z","volume":13,"title":"Application of the Moser–Trudinger inequality in the construction of global solutions to a strongly degenerate migration model","doi":"10.1142/s1664360722500126","type":"journal_article","publication":"Bulletin of Mathematical Sciences","abstract":[{"lang":"eng","text":" A no-flux initial-boundary value problem for the cross-diffusion system [Formula: see text] is considered in smoothly bounded domains [Formula: see text] with [Formula: see text]. It is shown that whenever [Formula: see text] is positive on [Formula: see text] and such that [Formula: see text] for some [Formula: see text], for all suitably regular positive initial data a global very weak solution, particularly preserving mass in its first component, can be constructed. This extends previous results which either concentrate on non-degenerate analogs, or are restricted to the special case [Formula: see text]. To appropriately cope with the considerably stronger cross-degeneracies thus allowed through [Formula: see text] when [Formula: see text] is large, in its core part the analysis relies on the use of the Moser–Trudinger inequality in controlling the respective diffusion rates [Formula: see text] from below. "}],"status":"public","_id":"63284","user_id":"31496","article_number":"2250012","language":[{"iso":"eng"}]},{"_id":"63286","user_id":"31496","language":[{"iso":"eng"}],"type":"journal_article","publication":"Asymptotic Analysis","abstract":[{"lang":"eng","text":" The chemotaxis system [Formula: see text] is considered in a ball [Formula: see text]. It is shown that if [Formula: see text] suitably generalizes the prototype given by [Formula: see text] with some [Formula: see text], and if diffusion is suitably weak in the sense that [Formula: see text] is such that there exist [Formula: see text] and [Formula: see text] fulfilling [Formula: see text] then for appropriate choices of sufficiently concentrated initial data, an associated no-flux initial-boundary value problem admits a global classical solution [Formula: see text] which blows up in infinite time and satisfies [Formula: see text] A major part of the proof is based on a comparison argument involving explicitly constructed subsolutions to a scalar parabolic problem satisfied by mass accumulation functions corresponding to solutions of ( ⋆ ). "}],"status":"public","publisher":"SAGE Publications","date_updated":"2025-12-18T20:07:19Z","date_created":"2025-12-18T19:18:51Z","author":[{"full_name":"Winkler, Michael","id":"31496","last_name":"Winkler","first_name":"Michael"}],"volume":131,"title":"Exponential grow-up rates in a quasilinear Keller–Segel system","doi":"10.3233/asy-221765","publication_status":"published","publication_identifier":{"issn":["0921-7134","1875-8576"]},"issue":"1","year":"2022","citation":{"apa":"Winkler, M. (2022). Exponential grow-up rates in a quasilinear Keller–Segel system. Asymptotic Analysis, 131(1), 33–57. https://doi.org/10.3233/asy-221765","mla":"Winkler, Michael. “Exponential Grow-up Rates in a Quasilinear Keller–Segel System.” Asymptotic Analysis, vol. 131, no. 1, SAGE Publications, 2022, pp. 33–57, doi:10.3233/asy-221765.","bibtex":"@article{Winkler_2022, title={Exponential grow-up rates in a quasilinear Keller–Segel system}, volume={131}, DOI={10.3233/asy-221765}, number={1}, journal={Asymptotic Analysis}, publisher={SAGE Publications}, author={Winkler, Michael}, year={2022}, pages={33–57} }","short":"M. Winkler, Asymptotic Analysis 131 (2022) 33–57.","ieee":"M. Winkler, “Exponential grow-up rates in a quasilinear Keller–Segel system,” Asymptotic Analysis, vol. 131, no. 1, pp. 33–57, 2022, doi: 10.3233/asy-221765.","chicago":"Winkler, Michael. “Exponential Grow-up Rates in a Quasilinear Keller–Segel System.” Asymptotic Analysis 131, no. 1 (2022): 33–57. https://doi.org/10.3233/asy-221765.","ama":"Winkler M. Exponential grow-up rates in a quasilinear Keller–Segel system. Asymptotic Analysis. 2022;131(1):33-57. doi:10.3233/asy-221765"},"page":"33-57","intvolume":" 131"},{"doi":"10.3934/dcds.2022091","title":"Global weak solutions to a chemotaxis-Navier-Stokes system in $ \\mathbb{R}^3 $","date_created":"2025-12-18T19:22:04Z","author":[{"first_name":"Kyungkeun","last_name":"Kang","full_name":"Kang, Kyungkeun"},{"first_name":"Jihoon","last_name":"Lee","full_name":"Lee, Jihoon"},{"last_name":"Winkler","id":"31496","full_name":"Winkler, Michael","first_name":"Michael"}],"volume":42,"date_updated":"2025-12-18T20:08:21Z","publisher":"American Institute of Mathematical Sciences (AIMS)","citation":{"ama":"Kang K, Lee J, Winkler M. Global weak solutions to a chemotaxis-Navier-Stokes system in $  \\mathbb{R}^3 $. Discrete and Continuous Dynamical Systems. 2022;42(11). doi:10.3934/dcds.2022091","ieee":"K. Kang, J. Lee, and M. Winkler, “Global weak solutions to a chemotaxis-Navier-Stokes system in $  \\mathbb{R}^3 $,” Discrete and Continuous Dynamical Systems, vol. 42, no. 11, Art. no. 5201, 2022, doi: 10.3934/dcds.2022091.","chicago":"Kang, Kyungkeun, Jihoon Lee, and Michael Winkler. “Global Weak Solutions to a Chemotaxis-Navier-Stokes System in $  \\mathbb{R}^3 $.” Discrete and Continuous Dynamical Systems 42, no. 11 (2022). https://doi.org/10.3934/dcds.2022091.","short":"K. Kang, J. Lee, M. Winkler, Discrete and Continuous Dynamical Systems 42 (2022).","bibtex":"@article{Kang_Lee_Winkler_2022, title={Global weak solutions to a chemotaxis-Navier-Stokes system in $  \\mathbb{R}^3 $}, volume={42}, DOI={10.3934/dcds.2022091}, number={115201}, journal={Discrete and Continuous Dynamical Systems}, publisher={American Institute of Mathematical Sciences (AIMS)}, author={Kang, Kyungkeun and Lee, Jihoon and Winkler, Michael}, year={2022} }","mla":"Kang, Kyungkeun, et al. “Global Weak Solutions to a Chemotaxis-Navier-Stokes System in $  \\mathbb{R}^3 $.” Discrete and Continuous Dynamical Systems, vol. 42, no. 11, 5201, American Institute of Mathematical Sciences (AIMS), 2022, doi:10.3934/dcds.2022091.","apa":"Kang, K., Lee, J., & Winkler, M. (2022). Global weak solutions to a chemotaxis-Navier-Stokes system in $  \\mathbb{R}^3 $. Discrete and Continuous Dynamical Systems, 42(11), Article 5201. https://doi.org/10.3934/dcds.2022091"},"intvolume":" 42","year":"2022","issue":"11","publication_status":"published","publication_identifier":{"issn":["1078-0947","1553-5231"]},"language":[{"iso":"eng"}],"article_number":"5201","user_id":"31496","_id":"63293","status":"public","abstract":[{"text":"<p style='text-indent:20px;'>The Cauchy problem in <inline-formula><tex-math id=\"M2\">\\begin{document}$ \\mathbb{R}^3 $\\end{document}</tex-math></inline-formula> for the chemotaxis-Navier–Stokes system</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id=\"FE1\"> \\begin{document}$ \\begin{eqnarray*} \\left\\{ \\begin{array}{l} n_t + u\\cdot\\nabla n = \\Delta n - \\nabla \\cdot (n\\nabla c), \\\\\tc_t + u\\cdot\\nabla c = \\Delta c - nc, \\\\ \tu_t + (u\\cdot\\nabla) u = \\Delta u + \\nabla P + n\\nabla\\phi, \\qquad \\nabla \\cdot u = 0, \\ \t\\end{array} \\right. \\end{eqnarray*} $\\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>is considered. Under suitable conditions on the initial data <inline-formula><tex-math id=\"M3\">\\begin{document}$ (n_0, c_0, u_0) $\\end{document}</tex-math></inline-formula>, with regard to the crucial first component requiring that <inline-formula><tex-math id=\"M4\">\\begin{document}$ n_0\\in L^1( \\mathbb{R}^3) $\\end{document}</tex-math></inline-formula> be nonnegative and such that <inline-formula><tex-math id=\"M5\">\\begin{document}$ (n_0+1)\\ln (n_0+1) \\in L^1( \\mathbb{R}^3) $\\end{document}</tex-math></inline-formula>, a globally defined weak solution with <inline-formula><tex-math id=\"M6\">\\begin{document}$ (n, c, u)|_{t = 0} = (n_0, c_0, u_0) $\\end{document}</tex-math></inline-formula> is constructed. Apart from that, assuming that moreover <inline-formula><tex-math id=\"M7\">\\begin{document}$ \\int_{ \\mathbb{R}^3} n_0(x) \\ln (1+|x|^2) dx $\\end{document}</tex-math></inline-formula> is finite, it is shown that a weak solution exists which enjoys further regularity features and preserves mass in an appropriate sense.</p>","lang":"eng"}],"type":"journal_article","publication":"Discrete and Continuous Dynamical Systems"},{"year":"2022","intvolume":" 32","page":"713-792","citation":{"mla":"Bellomo, N., et al. “Chemotaxis and Cross-Diffusion Models in Complex Environments: Models and Analytic Problems toward a Multiscale Vision.” Mathematical Models and Methods in Applied Sciences, vol. 32, no. 04, World Scientific Pub Co Pte Ltd, 2022, pp. 713–92, doi:10.1142/s0218202522500166.","short":"N. Bellomo, N. Outada, J. Soler, Y. Tao, M. Winkler, Mathematical Models and Methods in Applied Sciences 32 (2022) 713–792.","bibtex":"@article{Bellomo_Outada_Soler_Tao_Winkler_2022, title={Chemotaxis and cross-diffusion models in complex environments: Models and analytic problems toward a multiscale vision}, volume={32}, DOI={10.1142/s0218202522500166}, number={04}, journal={Mathematical Models and Methods in Applied Sciences}, publisher={World Scientific Pub Co Pte Ltd}, author={Bellomo, N. and Outada, N. and Soler, J. and Tao, Y. and Winkler, Michael}, year={2022}, pages={713–792} }","apa":"Bellomo, N., Outada, N., Soler, J., Tao, Y., & Winkler, M. (2022). Chemotaxis and cross-diffusion models in complex environments: Models and analytic problems toward a multiscale vision. Mathematical Models and Methods in Applied Sciences, 32(04), 713–792. https://doi.org/10.1142/s0218202522500166","ama":"Bellomo N, Outada N, Soler J, Tao Y, Winkler M. Chemotaxis and cross-diffusion models in complex environments: Models and analytic problems toward a multiscale vision. Mathematical Models and Methods in Applied Sciences. 2022;32(04):713-792. doi:10.1142/s0218202522500166","ieee":"N. Bellomo, N. Outada, J. Soler, Y. Tao, and M. Winkler, “Chemotaxis and cross-diffusion models in complex environments: Models and analytic problems toward a multiscale vision,” Mathematical Models and Methods in Applied Sciences, vol. 32, no. 04, pp. 713–792, 2022, doi: 10.1142/s0218202522500166.","chicago":"Bellomo, N., N. Outada, J. Soler, Y. Tao, and Michael Winkler. “Chemotaxis and Cross-Diffusion Models in Complex Environments: Models and Analytic Problems toward a Multiscale Vision.” Mathematical Models and Methods in Applied Sciences 32, no. 04 (2022): 713–92. https://doi.org/10.1142/s0218202522500166."},"publication_identifier":{"issn":["0218-2025","1793-6314"]},"publication_status":"published","issue":"04","title":"Chemotaxis and cross-diffusion models in complex environments: Models and analytic problems toward a multiscale vision","doi":"10.1142/s0218202522500166","date_updated":"2025-12-18T20:07:51Z","publisher":"World Scientific Pub Co Pte Ltd","volume":32,"date_created":"2025-12-18T19:20:25Z","author":[{"first_name":"N.","last_name":"Bellomo","full_name":"Bellomo, N."},{"first_name":"N.","full_name":"Outada, N.","last_name":"Outada"},{"last_name":"Soler","full_name":"Soler, J.","first_name":"J."},{"full_name":"Tao, Y.","last_name":"Tao","first_name":"Y."},{"last_name":"Winkler","id":"31496","full_name":"Winkler, Michael","first_name":"Michael"}],"abstract":[{"lang":"eng","text":" This paper proposes a review focused on exotic chemotaxis and cross-diffusion models in complex environments. The term exotic is used to denote the dynamics of models interacting with a time-evolving external system and, specifically, models derived with the aim of describing the dynamics of living systems. The presentation first, considers the derivation of phenomenological models of chemotaxis and cross-diffusion models with particular attention on nonlinear characteristics. Then, a variety of exotic models is presented with some hints toward the derivation of new models, by accounting for a critical analysis looking ahead to perspectives. The second part of the paper is devoted to a survey of analytical problems concerning the application of models to the study of real world dynamics. Finally, the focus shifts to research perspectives within the framework of a multiscale vision, where different paths are examined to move from the dynamics at the microscopic scale to collective behaviors at the macroscopic scale. "}],"status":"public","publication":"Mathematical Models and Methods in Applied Sciences","type":"journal_article","language":[{"iso":"eng"}],"_id":"63290","user_id":"31496"},{"author":[{"first_name":"Johannes","last_name":"Lankeit","full_name":"Lankeit, Johannes"},{"first_name":"Michael","id":"31496","full_name":"Winkler, Michael","last_name":"Winkler"}],"date_created":"2025-12-18T19:22:46Z","volume":22,"date_updated":"2025-12-18T20:08:35Z","publisher":"Springer Science and Business Media LLC","doi":"10.1007/s00028-022-00768-9","title":"Global existence in reaction–diffusion systems with mass control under relaxed assumptions merely referring to cross-absorptive effects","issue":"1","publication_status":"published","publication_identifier":{"issn":["1424-3199","1424-3202"]},"citation":{"ieee":"J. Lankeit and M. Winkler, “Global existence in reaction–diffusion systems with mass control under relaxed assumptions merely referring to cross-absorptive effects,” Journal of Evolution Equations, vol. 22, no. 1, Art. no. 14, 2022, doi: 10.1007/s00028-022-00768-9.","chicago":"Lankeit, Johannes, and Michael Winkler. “Global Existence in Reaction–Diffusion Systems with Mass Control under Relaxed Assumptions Merely Referring to Cross-Absorptive Effects.” Journal of Evolution Equations 22, no. 1 (2022). https://doi.org/10.1007/s00028-022-00768-9.","ama":"Lankeit J, Winkler M. Global existence in reaction–diffusion systems with mass control under relaxed assumptions merely referring to cross-absorptive effects. Journal of Evolution Equations. 2022;22(1). doi:10.1007/s00028-022-00768-9","apa":"Lankeit, J., & Winkler, M. (2022). Global existence in reaction–diffusion systems with mass control under relaxed assumptions merely referring to cross-absorptive effects. Journal of Evolution Equations, 22(1), Article 14. https://doi.org/10.1007/s00028-022-00768-9","short":"J. Lankeit, M. Winkler, Journal of Evolution Equations 22 (2022).","bibtex":"@article{Lankeit_Winkler_2022, title={Global existence in reaction–diffusion systems with mass control under relaxed assumptions merely referring to cross-absorptive effects}, volume={22}, DOI={10.1007/s00028-022-00768-9}, number={114}, journal={Journal of Evolution Equations}, publisher={Springer Science and Business Media LLC}, author={Lankeit, Johannes and Winkler, Michael}, year={2022} }","mla":"Lankeit, Johannes, and Michael Winkler. “Global Existence in Reaction–Diffusion Systems with Mass Control under Relaxed Assumptions Merely Referring to Cross-Absorptive Effects.” Journal of Evolution Equations, vol. 22, no. 1, 14, Springer Science and Business Media LLC, 2022, doi:10.1007/s00028-022-00768-9."},"intvolume":" 22","year":"2022","user_id":"31496","_id":"63295","language":[{"iso":"eng"}],"article_number":"14","type":"journal_article","publication":"Journal of Evolution Equations","status":"public","abstract":[{"text":"AbstractWe introduce a generalized concept of solutions for reaction–diffusion systems and prove their global existence. The only restriction on the reaction function beyond regularity, quasipositivity and mass control is special in that it merely controls the growth of cross-absorptive terms. The result covers nonlinear diffusion and does not rely on an entropy estimate.","lang":"eng"}]}]