[{"related_material":{"link":[{"url":"https://doi.org/10.1088/2515-7647/acc70c","description":"Corrigendum for table C1","relation":"erratum"}]},"publication_identifier":{"issn":["2515-7647"]},"publication_status":"published","page":"025001","intvolume":" 4","citation":{"bibtex":"@article{Ebers_Ferreri_Hammer_Albert_Meier_Förstner_Sharapova_2022, title={Flexible source of correlated photons based on LNOI rib waveguides}, volume={4}, DOI={10.1088/2515-7647/ac5a5b}, journal={Journal of Physics: Photonics}, publisher={IOP Publishing}, author={Ebers, Lena and Ferreri, Alessandro and Hammer, Manfred and Albert, Maximilian and Meier, Cedrik and Förstner, Jens and Sharapova, Polina R.}, year={2022}, pages={025001} }","short":"L. Ebers, A. Ferreri, M. Hammer, M. Albert, C. Meier, J. Förstner, P.R. Sharapova, Journal of Physics: Photonics 4 (2022) 025001.","mla":"Ebers, Lena, et al. “Flexible Source of Correlated Photons Based on LNOI Rib Waveguides.” Journal of Physics: Photonics, vol. 4, IOP Publishing, 2022, p. 025001, doi:10.1088/2515-7647/ac5a5b.","apa":"Ebers, L., Ferreri, A., Hammer, M., Albert, M., Meier, C., Förstner, J., & Sharapova, P. R. (2022). Flexible source of correlated photons based on LNOI rib waveguides. Journal of Physics: Photonics, 4, 025001. https://doi.org/10.1088/2515-7647/ac5a5b","chicago":"Ebers, Lena, Alessandro Ferreri, Manfred Hammer, Maximilian Albert, Cedrik Meier, Jens Förstner, and Polina R. Sharapova. “Flexible Source of Correlated Photons Based on LNOI Rib Waveguides.” Journal of Physics: Photonics 4 (2022): 025001. https://doi.org/10.1088/2515-7647/ac5a5b.","ieee":"L. Ebers et al., “Flexible source of correlated photons based on LNOI rib waveguides,” Journal of Physics: Photonics, vol. 4, p. 025001, 2022, doi: 10.1088/2515-7647/ac5a5b.","ama":"Ebers L, Ferreri A, Hammer M, et al. Flexible source of correlated photons based on LNOI rib waveguides. Journal of Physics: Photonics. 2022;4:025001. doi:10.1088/2515-7647/ac5a5b"},"year":"2022","volume":4,"author":[{"last_name":"Ebers","id":"40428","full_name":"Ebers, Lena","first_name":"Lena"},{"last_name":"Ferreri","full_name":"Ferreri, Alessandro","id":"65609","first_name":"Alessandro"},{"first_name":"Manfred","full_name":"Hammer, Manfred","id":"48077","last_name":"Hammer","orcid":"0000-0002-6331-9348"},{"first_name":"Maximilian","last_name":"Albert","full_name":"Albert, Maximilian"},{"first_name":"Cedrik","orcid":"https://orcid.org/0000-0002-3787-3572","last_name":"Meier","full_name":"Meier, Cedrik","id":"20798"},{"first_name":"Jens","id":"158","full_name":"Förstner, Jens","last_name":"Förstner","orcid":"0000-0001-7059-9862"},{"first_name":"Polina R.","full_name":"Sharapova, Polina R.","id":"60286","last_name":"Sharapova"}],"date_created":"2022-03-07T09:51:50Z","date_updated":"2025-12-16T11:31:04Z","publisher":"IOP Publishing","doi":"10.1088/2515-7647/ac5a5b","title":"Flexible source of correlated photons based on LNOI rib waveguides","publication":"Journal of Physics: Photonics","type":"journal_article","status":"public","abstract":[{"lang":"eng","text":"Lithium niobate on insulator (LNOI) has a great potential for photonic integrated circuits, providing substantial versatility in design of various integrated components. To properly use these components in the implementation of different quantum protocols, photons with different properties are required. In this paper, we theoretically demonstrate a flexible source of correlated photons built on the LNOI waveguide of a special geometry. This source is based on the parametric down-conversion (PDC) process, in which the signal and idler photons are generated at the telecom wavelength and have different spatial profiles and polarizations, but the same group velocities. Distinguishability in polarizations and spatial profiles facilitates the routing and manipulating individual photons, while the equality of their group velocities leads to the absence of temporal walk-off between photons. We show how the spectral properties of the generated photons and the number of their frequency modes can be controlled depending on the pump characteristics and the waveguide length. Finally, we discuss special regimes, in which narrowband light with strong frequency correlations and polarization-entangled Bell states are generated at the telecom wavelength."}],"department":[{"_id":"61"},{"_id":"230"},{"_id":"429"},{"_id":"15"},{"_id":"569"},{"_id":"170"},{"_id":"287"},{"_id":"35"},{"_id":"34"}],"user_id":"16199","_id":"30210","project":[{"name":"TRR 142 - C: TRR 142 - Project Area C","_id":"56"},{"name":"TRR 142 - C5: TRR 142 - Subproject C5","_id":"75"},{"_id":"72","name":"TRR 142 - C2: TRR 142 - Subproject C2"},{"name":"TRR 142: TRR 142","_id":"53"},{"name":"TRR 142: Maßgeschneiderte nichtlineare Photonik: Von grundlegenden Konzepten zu funktionellen Strukturen","_id":"53"}],"language":[{"iso":"eng"}],"keyword":["tet_topic_waveguide"]},{"intvolume":" 318","page":"275-293","citation":{"apa":"Iyengar, S. B., Letz, J. C., Liu, J., & Pollitz, J. (2022). Exceptional complete intersection maps of local rings. Pacific J. Math., 318(2), 275–293. https://doi.org/10.2140/pjm.2022.318.275","short":"S.B. Iyengar, J.C. Letz, J. Liu, J. Pollitz, Pacific J. Math. 318 (2022) 275–293.","bibtex":"@article{Iyengar_Letz_Liu_Pollitz_2022, title={Exceptional complete intersection maps of local rings}, volume={318}, DOI={10.2140/pjm.2022.318.275}, number={2}, journal={Pacific J. Math.}, author={Iyengar, Srikanth B. and Letz, Janina Carmen and Liu, Jian and Pollitz, Josh}, year={2022}, pages={275–293} }","mla":"Iyengar, Srikanth B., et al. “Exceptional Complete Intersection Maps of Local Rings.” Pacific J. Math., vol. 318, no. 2, 2022, pp. 275–93, doi:10.2140/pjm.2022.318.275.","ama":"Iyengar SB, Letz JC, Liu J, Pollitz J. Exceptional complete intersection maps of local rings. Pacific J Math. 2022;318(2):275-293. doi:10.2140/pjm.2022.318.275","chicago":"Iyengar, Srikanth B., Janina Carmen Letz, Jian Liu, and Josh Pollitz. “Exceptional Complete Intersection Maps of Local Rings.” Pacific J. Math. 318, no. 2 (2022): 275–93. https://doi.org/10.2140/pjm.2022.318.275.","ieee":"S. B. Iyengar, J. C. Letz, J. Liu, and J. Pollitz, “Exceptional complete intersection maps of local rings,” Pacific J. Math., vol. 318, no. 2, pp. 275–293, 2022, doi: 10.2140/pjm.2022.318.275."},"year":"2022","issue":"2","publication_identifier":{"issn":["0030-8730"]},"doi":"10.2140/pjm.2022.318.275","title":"Exceptional complete intersection maps of local rings","volume":318,"author":[{"full_name":"Iyengar, Srikanth B.","last_name":"Iyengar","first_name":"Srikanth B."},{"id":"121953","full_name":"Letz, Janina Carmen","orcid":"0000-0002-5497-8296","last_name":"Letz","first_name":"Janina Carmen"},{"first_name":"Jian","last_name":"Liu","full_name":"Liu, Jian"},{"last_name":"Pollitz","full_name":"Pollitz, Josh","first_name":"Josh"}],"date_created":"2025-12-16T14:28:18Z","date_updated":"2025-12-16T14:44:02Z","status":"public","publication":"Pacific J. Math.","type":"journal_article","extern":"1","language":[{"iso":"eng"}],"user_id":"121953","_id":"63139"},{"language":[{"iso":"eng"}],"extern":"1","alternative_title":["Themenheft zur 20. Jahrestagung der Gesellschaft für Aphasieforschung und –behandlung. Neurologie & Rehabilitation. "],"department":[{"_id":"5"},{"_id":"890"}],"user_id":"94540","_id":"55135","status":"public","editor":[{"id":"94540","full_name":"Jonas, Kristina","last_name":"Jonas","orcid":"0000-0002-1067-9139","first_name":"Kristina"},{"last_name":"Quinting","full_name":"Quinting, Jana","first_name":"Jana"},{"first_name":"Lisa","last_name":"Gerhards","full_name":"Gerhards, Lisa"},{"first_name":"Anne","last_name":"Hüsgen","full_name":"Hüsgen, Anne"},{"first_name":"Ilona","full_name":"Rubi-Fessen, Ilona","last_name":"Rubi-Fessen"},{"full_name":"Stenneken, Prisca","last_name":"Stenneken","first_name":"Prisca"},{"first_name":"Anna","full_name":"Rosenkranz, Anna","last_name":"Rosenkranz"}],"type":"conference_editor","title":"Kommunikation – Sprache, Emotion, Kognition","date_created":"2024-07-08T11:24:56Z","date_updated":"2025-12-17T07:34:41Z","citation":{"chicago":"Jonas, Kristina, Jana Quinting, Lisa Gerhards, Anne Hüsgen, Ilona Rubi-Fessen, Prisca Stenneken, and Anna Rosenkranz, eds. Kommunikation – Sprache, Emotion, Kognition, 2022.","ieee":"K. Jonas et al., Eds., Kommunikation – Sprache, Emotion, Kognition. 2022.","ama":"Jonas K, Quinting J, Gerhards L, et al., eds. Kommunikation – Sprache, Emotion, Kognition.; 2022.","short":"K. Jonas, J. Quinting, L. Gerhards, A. Hüsgen, I. Rubi-Fessen, P. Stenneken, A. Rosenkranz, eds., Kommunikation – Sprache, Emotion, Kognition, 2022.","mla":"Jonas, Kristina, et al., editors. Kommunikation – Sprache, Emotion, Kognition. 2022.","bibtex":"@book{Jonas_Quinting_Gerhards_Hüsgen_Rubi-Fessen_Stenneken_Rosenkranz_2022, title={Kommunikation – Sprache, Emotion, Kognition}, year={2022} }","apa":"Jonas, K., Quinting, J., Gerhards, L., Hüsgen, A., Rubi-Fessen, I., Stenneken, P., & Rosenkranz, A. (Eds.). (2022). Kommunikation – Sprache, Emotion, Kognition."},"year":"2022"},{"date_created":"2025-12-17T08:53:34Z","author":[{"first_name":"S","full_name":"Barlovits, S","last_name":"Barlovits"},{"last_name":"Caldeira","full_name":"Caldeira, A","first_name":"A"},{"last_name":"Fesakis","full_name":"Fesakis, G","first_name":"G"},{"last_name":"Jablonski","full_name":"Jablonski, S","first_name":"S"},{"last_name":"Filippaki","full_name":"Filippaki, DK","first_name":"DK"},{"first_name":"C","last_name":"Lázaro","full_name":"Lázaro, C"},{"first_name":"M","last_name":"Ludwig","full_name":"Ludwig, M"},{"first_name":"MF","last_name":"Mammana","full_name":"Mammana, MF"},{"last_name":"Moura","full_name":"Moura, A","first_name":"A"},{"full_name":"Oehler, DXK","last_name":"Oehler","first_name":"DXK"},{"first_name":"T","last_name":"Recio","full_name":"Recio, T"},{"full_name":"Taranto, E","last_name":"Taranto","first_name":"E"},{"first_name":"S","last_name":"Volika","full_name":"Volika, S"}],"volume":10,"date_updated":"2025-12-17T08:56:18Z","title":"Adaptive, Synchronous, and Mobile Online Education: Developing the ASYMPTOTE Learning Environment","issue":"10","publication_status":"published","quality_controlled":"1","publication_identifier":{"issn":["2227-7390"]},"citation":{"ama":"Barlovits S, Caldeira A, Fesakis G, et al. Adaptive, Synchronous, and Mobile Online Education: Developing the ASYMPTOTE Learning Environment. 2022;10(10).","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).","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).","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).","mla":"Barlovits, S., et al. Adaptive, Synchronous, and Mobile Online Education: Developing the ASYMPTOTE Learning Environment. no. 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} }"},"intvolume":" 10","year":"2022","user_id":"111489","_id":"63175","type":"journal_article","status":"public"},{"status":"public","type":"journal_article","_id":"63174","user_id":"111489","year":"2022","intvolume":" 12","citation":{"apa":"Barbosa, A., Vale, I., Jablonski, S., & Ludwig, M. (2022). Walking through Algebraic Thinking with Theme-Based (Mobile) Math Trails. 12(5).","mla":"Barbosa, A., et al. Walking through Algebraic Thinking with Theme-Based (Mobile) Math Trails. no. 5, 2022.","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).","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)."},"publication_identifier":{"issn":["2227-7102"]},"quality_controlled":"1","publication_status":"published","issue":"5","title":"Walking through Algebraic Thinking with Theme-Based (Mobile) Math Trails","date_updated":"2025-12-17T08:56:22Z","volume":12,"date_created":"2025-12-17T08:53:34Z","author":[{"last_name":"Barbosa","full_name":"Barbosa, A","first_name":"A"},{"first_name":"I","last_name":"Vale","full_name":"Vale, I"},{"last_name":"Jablonski","full_name":"Jablonski, S","first_name":"S"},{"first_name":"M","full_name":"Ludwig, M","last_name":"Ludwig"}]},{"department":[{"_id":"233"},{"_id":"716"}],"series_title":" Münsteraner Schriften zur zeitgenössischen Musik","user_id":"90389","_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":[{"full_name":"Höink, Dominik","id":"90389","last_name":"Höink","first_name":"Dominik"}],"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","page":"590","intvolume":" 8","citation":{"apa":"Höink, D. (2022). Oratorium und Nation (1914–1945) (Vol. 8). Waxmann Verlag.","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} }","mla":"Höink, Dominik. Oratorium und Nation (1914–1945) . Waxmann Verlag, 2022.","short":"D. Höink, Oratorium und Nation (1914–1945) , Waxmann Verlag, Münster, 2022.","ieee":"D. Höink, Oratorium und Nation (1914–1945) , vol. 8. Münster: Waxmann Verlag, 2022.","chicago":"Höink, Dominik. Oratorium und Nation (1914–1945) . Vol. 8. Münsteraner Schriften zur zeitgenössischen Musik. Münster: Waxmann Verlag, 2022.","ama":"Höink D. Oratorium und Nation (1914–1945) . Vol 8. Waxmann Verlag; 2022."},"year":"2022","place":"Münster"},{"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"}],"publication":"Époque Émilienne Philosophy and Science in the Age of Émilie Du Châtelet (1706-1749)","keyword":["Émilie Du Châtelet","History of Science","Newton","Kant","Eberhard","Wolff","Leibniz"],"language":[{"iso":"eng"}],"year":"2022","quality_controlled":"1","title":"Du Châtelet and Kant: Claiming the Renewal of Philosophy","publisher":"Springer International Publishing","date_created":"2022-12-21T11:35:14Z","editor":[{"first_name":"Ruth Edith","full_name":"Hagengruber, Ruth Edith","last_name":"Hagengruber"}],"status":"public","type":"book_chapter","_id":"34705","department":[{"_id":"615"},{"_id":"14"},{"_id":"519"}],"user_id":"91827","series_title":"Women in the History of Philosophy and Science ","place":"Cham","intvolume":" 10","page":"57-84","citation":{"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.","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.","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","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","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.","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 } }","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."},"publication_identifier":{"issn":["2523-8760","2523-8779"],"isbn":["9783030899202","9783030899219"]},"publication_status":"published","doi":"10.1007/978-3-030-89921-9_3","date_updated":"2025-12-17T13:40:24Z","volume":10,"author":[{"first_name":"Ruth Edith","orcid":"https://orcid.org/0000-0003-3360-6335","last_name":"Hagengruber","full_name":"Hagengruber, Ruth Edith","id":"198"}]},{"status":"public","editor":[{"last_name":"Hagengruber","full_name":"Hagengruber, Ruth Edith","first_name":"Ruth Edith"}],"type":"book_chapter","series_title":"Women in the History of Philosophy and Science ","user_id":"91827","department":[{"_id":"14"}],"_id":"63184","citation":{"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.","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 } }","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","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.","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.","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"},"page":"1-20","intvolume":" 10","place":"Cham","publication_status":"published","publication_identifier":{"isbn":["9783030899202","9783030899219"],"issn":["2523-8760","2523-8779"]},"doi":"10.1007/978-3-030-89921-9_1","author":[{"first_name":"Ruth","last_name":"Hagengruber","orcid":"https://orcid.org/0000-0003-3360-6335","full_name":"Hagengruber, Ruth","id":"198"}],"volume":10,"date_updated":"2025-12-17T13:38:49Z","publication":"Époque Émilienne Philosophy and Science in the Age of Émilie Du Châtelet (1706-1749)","language":[{"iso":"eng"}],"year":"2022","title":"An Introduction to the Volume","date_created":"2025-12-17T13:29:05Z","publisher":"Springer International Publishing"},{"abstract":[{"lang":"eng","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."}],"status":"public","type":"journal_article","publication":"npj Materials Degradation","article_number":"18","language":[{"iso":"eng"}],"_id":"63206","user_id":"7266","department":[{"_id":"35"},{"_id":"302"},{"_id":"321"}],"year":"2022","citation":{"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.","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","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","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} }","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.","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)."},"intvolume":" 6","publication_status":"published","publication_identifier":{"issn":["2397-2106"]},"issue":"1","title":"Corrosion fatigue behavior of electron beam melted iron in simulated body fluid","doi":"10.1038/s41529-022-00226-4","date_updated":"2025-12-18T11:56:57Z","publisher":"Springer Science and Business Media LLC","author":[{"last_name":"Wackenrohr","full_name":"Wackenrohr, Steffen","first_name":"Steffen"},{"full_name":"Torrent, Christof Johannes Jaime","last_name":"Torrent","first_name":"Christof Johannes Jaime"},{"first_name":"Sebastian","last_name":"Herbst","full_name":"Herbst, Sebastian"},{"last_name":"Nürnberger","full_name":"Nürnberger, Florian","first_name":"Florian"},{"first_name":"Philipp","full_name":"Krooss, Philipp","last_name":"Krooss"},{"first_name":"Christoph","id":"7266","full_name":"Ebbert, Christoph","last_name":"Ebbert"},{"full_name":"Voigt, Markus","id":"15182","last_name":"Voigt","first_name":"Markus"},{"first_name":"Guido","last_name":"Grundmeier","id":"194","full_name":"Grundmeier, Guido"},{"full_name":"Niendorf, Thomas","last_name":"Niendorf","first_name":"Thomas"},{"first_name":"Hans Jürgen","full_name":"Maier, Hans Jürgen","last_name":"Maier"}],"date_created":"2025-12-18T11:55:16Z","volume":6},{"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","author":[{"first_name":"Timon","last_name":"Schapeler","orcid":"0000-0001-7652-1716","id":"55629","full_name":"Schapeler, Timon"},{"first_name":"Tim","full_name":"Bartley, Tim","id":"49683","last_name":"Bartley"}],"date_created":"2022-10-11T07:13:12Z","volume":106,"publisher":"American Physical Society (APS)","date_updated":"2025-12-18T17:07:12Z","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.","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.","short":"T. Schapeler, T. Bartley, Physical Review A 106 (2022).","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} }","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"},"intvolume":" 106","year":"2022","issue":"1","publication_status":"published","publication_identifier":{"issn":["2469-9926","2469-9934"]}},{"_id":"63234","user_id":"117722","article_number":"103452","language":[{"iso":"eng"}],"extern":"1","type":"journal_article","publication":"Advanced Powder Technology","status":"public","publisher":"Elsevier BV","date_updated":"2025-12-18T17:37:31Z","author":[{"first_name":"Jens","last_name":"Wiegmann","full_name":"Wiegmann, Jens"},{"first_name":"Christian","id":"117722","full_name":"Leppin, Christian","last_name":"Leppin"},{"first_name":"Arne","last_name":"Langhoff","full_name":"Langhoff, Arne"},{"last_name":"Schwaderer","full_name":"Schwaderer, Jan","first_name":"Jan"},{"last_name":"Beuermann","full_name":"Beuermann, Sabine","first_name":"Sabine"},{"first_name":"Diethelm","full_name":"Johannsmann, Diethelm","last_name":"Johannsmann"},{"first_name":"Alfred P.","full_name":"Weber, Alfred P.","last_name":"Weber"}],"date_created":"2025-12-18T17:22:31Z","volume":33,"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_status":"published","quality_controlled":"1","publication_identifier":{"issn":["0921-8831"]},"issue":"3","year":"2022","citation":{"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.","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","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","short":"J. Wiegmann, C. Leppin, A. Langhoff, J. Schwaderer, S. Beuermann, D. Johannsmann, A.P. Weber, Advanced Powder Technology 33 (2022).","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} }","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."},"intvolume":" 33"},{"extern":"1","user_id":"117722","_id":"63233","status":"public","type":"journal_article","doi":"10.1021/acs.analchem.2c01763","author":[{"first_name":"Christian","last_name":"Leppin","full_name":"Leppin, Christian","id":"117722"},{"first_name":"Arne","last_name":"Langhoff","full_name":"Langhoff, Arne"},{"full_name":"Johannsmann, Diethelm","last_name":"Johannsmann","first_name":"Diethelm"}],"volume":94,"date_updated":"2025-12-18T17:38:07Z","citation":{"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.","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.","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","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","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.","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} }","short":"C. Leppin, A. Langhoff, D. Johannsmann, Analytical Chemistry 94 (2022) 10227–10233."},"page":"10227-10233","intvolume":" 94","publication_status":"published","publication_identifier":{"issn":["0003-2700","1520-6882"]},"language":[{"iso":"eng"}],"publication":"Analytical Chemistry","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)","year":"2022","issue":"28","quality_controlled":"1"},{"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","publication":"Advanced Nonlinear Studies","type":"journal_article","language":[{"iso":"eng"}],"_id":"63310","user_id":"31496","year":"2022","page":"88-117","intvolume":" 22","citation":{"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.","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} }","short":"M. Winkler, Advanced Nonlinear Studies 22 (2022) 88–117.","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","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.","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.","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"},"publication_identifier":{"issn":["2169-0375"]},"publication_status":"published","issue":"1","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","publisher":"Walter de Gruyter GmbH","date_updated":"2025-12-18T20:05:30Z","volume":22,"date_created":"2025-12-18T19:29:40Z","author":[{"id":"31496","full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael"}]},{"user_id":"31496","_id":"63305","language":[{"iso":"eng"}],"article_number":"108","publication":"Calculus of Variations and Partial Differential Equations","type":"journal_article","status":"public","abstract":[{"lang":"eng","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 )."}],"volume":61,"author":[{"id":"31496","full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael"}],"date_created":"2025-12-18T19:26:32Z","date_updated":"2025-12-18T20:04:43Z","publisher":"Springer Science and Business Media LLC","doi":"10.1007/s00526-021-02168-2","title":"Stabilization of arbitrary structures in a doubly degenerate reaction-diffusion system modeling bacterial motion on a nutrient-poor agar","issue":"3","publication_identifier":{"issn":["0944-2669","1432-0835"]},"publication_status":"published","intvolume":" 61","citation":{"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","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} }","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.","short":"M. Winkler, Calculus of Variations and Partial Differential Equations 61 (2022).","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.","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"},"year":"2022"},{"_id":"63311","user_id":"31496","article_number":"47","language":[{"iso":"eng"}],"publication":"Partial Differential Equations and Applications","type":"journal_article","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"}],"status":"public","publisher":"Springer Science and Business Media LLC","date_updated":"2025-12-18T20:05:38Z","volume":3,"author":[{"last_name":"Winkler","id":"31496","full_name":"Winkler, Michael","first_name":"Michael"}],"date_created":"2025-12-18T19:30:04Z","title":"Oscillatory decay in a degenerate parabolic equation","doi":"10.1007/s42985-022-00186-z","publication_identifier":{"issn":["2662-2963","2662-2971"]},"publication_status":"published","issue":"4","year":"2022","intvolume":" 3","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","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.","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.","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"}},{"user_id":"31496","_id":"63312","language":[{"iso":"eng"}],"article_number":"6565","publication":"Discrete and Continuous Dynamical Systems - B","type":"journal_article","status":"public","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"}],"volume":27,"author":[{"last_name":"Winkler","id":"31496","full_name":"Winkler, Michael","first_name":"Michael"}],"date_created":"2025-12-18T19:30:32Z","publisher":"American Institute of Mathematical Sciences (AIMS)","date_updated":"2025-12-18T20:05:47Z","doi":"10.3934/dcdsb.2022009","title":"Approaching logarithmic singularities in quasilinear chemotaxis-consumption systems with signal-dependent sensitivities","issue":"11","publication_identifier":{"issn":["1531-3492","1553-524X"]},"publication_status":"published","intvolume":" 27","citation":{"short":"M. Winkler, Discrete and Continuous Dynamical Systems - B 27 (2022).","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} }","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.","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","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."},"year":"2022"},{"citation":{"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.","short":"M. Winkler, Mathematische Nachrichten 295 (2022) 1840–1862.","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} }","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","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"},"page":"1840-1862","intvolume":" 295","year":"2022","issue":"9","publication_status":"published","publication_identifier":{"issn":["0025-584X","1522-2616"]},"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","date_created":"2025-12-18T19:28:46Z","author":[{"first_name":"Michael","full_name":"Winkler, Michael","id":"31496","last_name":"Winkler"}],"volume":295,"publisher":"Wiley","date_updated":"2025-12-18T20:05:19Z","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."}],"type":"journal_article","publication":"Mathematische Nachrichten","language":[{"iso":"eng"}],"user_id":"31496","_id":"63309"},{"publication_identifier":{"issn":["0022-2518"]},"publication_status":"published","issue":"4","year":"2022","intvolume":" 71","page":"1437-1465","citation":{"short":"M. Winkler, Indiana University Mathematics Journal 71 (2022) 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.","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} }","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","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","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."},"publisher":"Indiana University Mathematics Journal","date_updated":"2025-12-18T20:04:53Z","volume":71,"date_created":"2025-12-18T19:26:56Z","author":[{"last_name":"Winkler","full_name":"Winkler, Michael","id":"31496","first_name":"Michael"}],"title":"A critical blow-up exponent for flux limiation in a Keller-Segel system","doi":"10.1512/iumj.2022.71.9042","publication":"Indiana University Mathematics Journal","type":"journal_article","status":"public","_id":"63306","user_id":"31496","language":[{"iso":"eng"}]},{"publication_status":"published","publication_identifier":{"issn":["1664-3607","1664-3615"]},"issue":"02","year":"2022","citation":{"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.","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.","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","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.","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"},"intvolume":" 13","publisher":"World Scientific Pub Co Pte Ltd","date_updated":"2025-12-18T20:07:05Z","date_created":"2025-12-18T19:18:11Z","author":[{"first_name":"Michael","last_name":"Winkler","id":"31496","full_name":"Winkler, Michael"}],"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"}]},{"issue":"1","publication_status":"published","publication_identifier":{"issn":["0921-7134","1875-8576"]},"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","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} }","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.","short":"M. Winkler, Asymptotic Analysis 131 (2022) 33–57.","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.","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.","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","year":"2022","author":[{"first_name":"Michael","id":"31496","full_name":"Winkler, Michael","last_name":"Winkler"}],"date_created":"2025-12-18T19:18:51Z","volume":131,"publisher":"SAGE Publications","date_updated":"2025-12-18T20:07:19Z","doi":"10.3233/asy-221765","title":"Exponential grow-up rates in a quasilinear Keller–Segel system","type":"journal_article","publication":"Asymptotic Analysis","status":"public","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 ( ⋆ ). "}],"user_id":"31496","_id":"63286","language":[{"iso":"eng"}]}]