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Gutiérrez, IEEE Signal Processing Letters 30 (2023) 923–926.","mla":"Santamaria, Ignacio, et al. “SNR Maximization in Beyond Diagonal RIS-Assisted Single and Multiple Antenna Links.” IEEE Signal Processing Letters, vol. 30, Institute of Electrical and Electronics Engineers (IEEE), 2023, pp. 923–26, doi:10.1109/lsp.2023.3296902.","ama":"Santamaria I, Soleymani M, Jorswieck E, Gutiérrez J. SNR Maximization in Beyond Diagonal RIS-Assisted Single and Multiple Antenna Links. IEEE Signal Processing Letters. 2023;30:923-926. doi:10.1109/lsp.2023.3296902","bibtex":"@article{Santamaria_Soleymani_Jorswieck_Gutiérrez_2023, title={SNR Maximization in Beyond Diagonal RIS-Assisted Single and Multiple Antenna Links}, volume={30}, DOI={10.1109/lsp.2023.3296902}, journal={IEEE Signal Processing Letters}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Santamaria, Ignacio and Soleymani, Mohammad and Jorswieck, Eduard and Gutiérrez, Jesús}, year={2023}, pages={923–926} }"},"_id":"53262","publisher":"Institute of Electrical and Electronics Engineers (IEEE)","page":"923-926","volume":30,"user_id":"67076","status":"public","date_created":"2024-04-05T09:01:21Z","department":[{"_id":"263"}],"keyword":["Applied Mathematics","Electrical and Electronic Engineering","Signal Processing"],"type":"journal_article","publication":"IEEE Signal Processing Letters","language":[{"iso":"eng"}],"doi":"10.1109/lsp.2023.3296902","author":[{"last_name":"Santamaria","first_name":"Ignacio","full_name":"Santamaria, Ignacio"},{"full_name":"Soleymani, Mohammad","last_name":"Soleymani","first_name":"Mohammad"},{"full_name":"Jorswieck, Eduard","last_name":"Jorswieck","first_name":"Eduard"},{"last_name":"Gutiérrez","first_name":"Jesús","full_name":"Gutiérrez, Jesús"}],"publication_identifier":{"issn":["1070-9908","1558-2361"]},"title":"SNR Maximization in Beyond Diagonal RIS-Assisted Single and Multiple Antenna Links","year":"2023","intvolume":" 30","publication_status":"published","date_updated":"2024-04-05T13:20:51Z"},{"citation":{"mla":"Soleymani, Mohammad, et al. “Optimization of Rate-Splitting Multiple Access in Beyond Diagonal RIS-Assisted URLLC Systems.” IEEE Transactions on Wireless Communications, Institute of Electrical and Electronics Engineers (IEEE), 2023, pp. 1–1, doi:10.1109/twc.2023.3324190.","bibtex":"@article{Soleymani_Santamaria_Jorswieck_Clerckx_2023, title={Optimization of Rate-Splitting Multiple Access in Beyond Diagonal RIS-assisted URLLC Systems}, DOI={10.1109/twc.2023.3324190}, journal={IEEE Transactions on Wireless Communications}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Soleymani, Mohammad and Santamaria, Ignacio and Jorswieck, Eduard and Clerckx, Bruno}, year={2023}, pages={1–1} }","ama":"Soleymani M, Santamaria I, Jorswieck E, Clerckx B. Optimization of Rate-Splitting Multiple Access in Beyond Diagonal RIS-assisted URLLC Systems. IEEE Transactions on Wireless Communications. Published online 2023:1-1. doi:10.1109/twc.2023.3324190","ieee":"M. Soleymani, I. Santamaria, E. Jorswieck, and B. Clerckx, “Optimization of Rate-Splitting Multiple Access in Beyond Diagonal RIS-assisted URLLC Systems,” IEEE Transactions on Wireless Communications, pp. 1–1, 2023, doi: 10.1109/twc.2023.3324190.","apa":"Soleymani, M., Santamaria, I., Jorswieck, E., & Clerckx, B. (2023). Optimization of Rate-Splitting Multiple Access in Beyond Diagonal RIS-assisted URLLC Systems. IEEE Transactions on Wireless Communications, 1–1. https://doi.org/10.1109/twc.2023.3324190","chicago":"Soleymani, Mohammad, Ignacio Santamaria, Eduard Jorswieck, and Bruno Clerckx. “Optimization of Rate-Splitting Multiple Access in Beyond Diagonal RIS-Assisted URLLC Systems.” IEEE Transactions on Wireless Communications, 2023, 1–1. https://doi.org/10.1109/twc.2023.3324190.","short":"M. Soleymani, I. Santamaria, E. Jorswieck, B. Clerckx, IEEE Transactions on Wireless Communications (2023) 1–1."},"publication":"IEEE Transactions on Wireless Communications","department":[{"_id":"263"}],"keyword":["Applied Mathematics","Electrical and Electronic Engineering","Computer Science Applications"],"type":"journal_article","date_created":"2024-04-05T09:01:04Z","publication_status":"published","date_updated":"2024-04-05T13:20:40Z","author":[{"full_name":"Soleymani, Mohammad","last_name":"Soleymani","first_name":"Mohammad"},{"full_name":"Santamaria, Ignacio","first_name":"Ignacio","last_name":"Santamaria"},{"full_name":"Jorswieck, Eduard","last_name":"Jorswieck","first_name":"Eduard"},{"last_name":"Clerckx","first_name":"Bruno","full_name":"Clerckx, Bruno"}],"publication_identifier":{"issn":["1536-1276","1558-2248"]},"status":"public","year":"2023","title":"Optimization of Rate-Splitting Multiple Access in Beyond Diagonal RIS-assisted URLLC Systems","user_id":"67076","doi":"10.1109/twc.2023.3324190","_id":"53261","language":[{"iso":"eng"}],"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","page":"1-1"},{"date_created":"2024-04-07T12:30:25Z","keyword":["Applied Mathematics","Control and Optimization","Modeling and Simulation"],"type":"journal_article","issue":"6","publication":"Evolution Equations and Control Theory","language":[{"iso":"eng"}],"doi":"10.3934/eect.2023031","title":"Global smooth solutions in a three-dimensional cross-diffusive SIS epidemic model with saturated taxis at large densities","year":"2023","publication_identifier":{"issn":["2163-2480"]},"author":[{"full_name":"Tao, Youshan","first_name":"Youshan","last_name":"Tao"},{"full_name":"Winkler, Michael","first_name":"Michael","last_name":"Winkler"}],"date_updated":"2024-04-07T12:36:17Z","publication_status":"published","intvolume":" 12","citation":{"ama":"Tao Y, Winkler M. Global smooth solutions in a three-dimensional cross-diffusive SIS epidemic model with saturated taxis at large densities. Evolution Equations and Control Theory. 2023;12(6):1676-1687. doi:10.3934/eect.2023031","bibtex":"@article{Tao_Winkler_2023, title={Global smooth solutions in a three-dimensional cross-diffusive SIS epidemic model with saturated taxis at large densities}, volume={12}, DOI={10.3934/eect.2023031}, number={6}, journal={Evolution Equations and Control Theory}, publisher={American Institute of Mathematical Sciences (AIMS)}, author={Tao, Youshan and Winkler, Michael}, year={2023}, pages={1676–1687} }","mla":"Tao, Youshan, and Michael Winkler. “Global Smooth Solutions in a Three-Dimensional Cross-Diffusive SIS Epidemic Model with Saturated Taxis at Large Densities.” Evolution Equations and Control Theory, vol. 12, no. 6, American Institute of Mathematical Sciences (AIMS), 2023, pp. 1676–87, doi:10.3934/eect.2023031.","short":"Y. Tao, M. Winkler, Evolution Equations and Control Theory 12 (2023) 1676–1687.","chicago":"Tao, Youshan, and Michael Winkler. “Global Smooth Solutions in a Three-Dimensional Cross-Diffusive SIS Epidemic Model with Saturated Taxis at Large Densities.” Evolution Equations and Control Theory 12, no. 6 (2023): 1676–87. https://doi.org/10.3934/eect.2023031.","apa":"Tao, Y., & Winkler, M. (2023). Global smooth solutions in a three-dimensional cross-diffusive SIS epidemic model with saturated taxis at large densities. Evolution Equations and Control Theory, 12(6), 1676–1687. https://doi.org/10.3934/eect.2023031","ieee":"Y. Tao and M. Winkler, “Global smooth solutions in a three-dimensional cross-diffusive SIS epidemic model with saturated taxis at large densities,” Evolution Equations and Control Theory, vol. 12, no. 6, pp. 1676–1687, 2023, doi: 10.3934/eect.2023031."},"page":"1676-1687","publisher":"American Institute of Mathematical Sciences (AIMS)","_id":"53317","user_id":"31496","volume":12,"status":"public"},{"citation":{"apa":"Winkler, M. (2023). A quantitative strong parabolic maximum principle and application to a taxis-type migration–consumption model involving signal-dependent degenerate diffusion. Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire. https://doi.org/10.4171/aihpc/73","ieee":"M. Winkler, “A quantitative strong parabolic maximum principle and application to a taxis-type migration–consumption model involving signal-dependent degenerate diffusion,” Annales de l’Institut Henri Poincaré C, Analyse non linéaire, 2023, doi: 10.4171/aihpc/73.","short":"M. Winkler, Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire (2023).","chicago":"Winkler, Michael. “A Quantitative Strong Parabolic Maximum Principle and Application to a Taxis-Type Migration–Consumption Model Involving Signal-Dependent Degenerate Diffusion.” Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire, 2023. https://doi.org/10.4171/aihpc/73.","mla":"Winkler, Michael. “A Quantitative Strong Parabolic Maximum Principle and Application to a Taxis-Type Migration–Consumption Model Involving Signal-Dependent Degenerate Diffusion.” Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire, European Mathematical Society - EMS - Publishing House GmbH, 2023, doi:10.4171/aihpc/73.","ama":"Winkler M. A quantitative strong parabolic maximum principle and application to a taxis-type migration–consumption model involving signal-dependent degenerate diffusion. Annales de l’Institut Henri Poincaré C, Analyse non linéaire. Published online 2023. doi:10.4171/aihpc/73","bibtex":"@article{Winkler_2023, title={A quantitative strong parabolic maximum principle and application to a taxis-type migration–consumption model involving signal-dependent degenerate diffusion}, DOI={10.4171/aihpc/73}, journal={Annales de l’Institut Henri Poincaré C, Analyse non linéaire}, publisher={European Mathematical Society - EMS - Publishing House GmbH}, author={Winkler, Michael}, year={2023} }"},"publication":"Annales de l'Institut Henri Poincaré C, Analyse non linéaire","keyword":["Mathematical Physics","Analysis","Applied Mathematics"],"type":"journal_article","date_created":"2024-04-07T12:34:35Z","publication_status":"published","date_updated":"2024-04-07T12:36:00Z","author":[{"first_name":"Michael","last_name":"Winkler","full_name":"Winkler, Michael"}],"publication_identifier":{"issn":["0294-1449","1873-1430"]},"year":"2023","status":"public","title":"A quantitative strong parabolic maximum principle and application to a taxis-type migration–consumption model involving signal-dependent degenerate diffusion","user_id":"31496","doi":"10.4171/aihpc/73","_id":"53320","language":[{"iso":"eng"}],"publisher":"European Mathematical Society - EMS - Publishing House GmbH"},{"status":"public","user_id":"31496","volume":103,"page":"45-64","_id":"53318","publisher":"Informa UK Limited","citation":{"mla":"Li, Genglin, and Michael Winkler. “Refined Regularity Analysis for a Keller-Segel-Consumption System Involving Signal-Dependent Motilities.” Applicable Analysis, vol. 103, no. 1, Informa UK Limited, 2023, pp. 45–64, doi:10.1080/00036811.2023.2173183.","ama":"Li G, Winkler M. Refined regularity analysis for a Keller-Segel-consumption system involving signal-dependent motilities. Applicable Analysis. 2023;103(1):45-64. doi:10.1080/00036811.2023.2173183","bibtex":"@article{Li_Winkler_2023, title={Refined regularity analysis for a Keller-Segel-consumption system involving signal-dependent motilities}, volume={103}, DOI={10.1080/00036811.2023.2173183}, number={1}, journal={Applicable Analysis}, publisher={Informa UK Limited}, author={Li, Genglin and Winkler, Michael}, year={2023}, pages={45–64} }","apa":"Li, G., & Winkler, M. (2023). Refined regularity analysis for a Keller-Segel-consumption system involving signal-dependent motilities. Applicable Analysis, 103(1), 45–64. https://doi.org/10.1080/00036811.2023.2173183","ieee":"G. Li and M. Winkler, “Refined regularity analysis for a Keller-Segel-consumption system involving signal-dependent motilities,” Applicable Analysis, vol. 103, no. 1, pp. 45–64, 2023, doi: 10.1080/00036811.2023.2173183.","short":"G. Li, M. Winkler, Applicable Analysis 103 (2023) 45–64.","chicago":"Li, Genglin, and Michael Winkler. “Refined Regularity Analysis for a Keller-Segel-Consumption System Involving Signal-Dependent Motilities.” Applicable Analysis 103, no. 1 (2023): 45–64. https://doi.org/10.1080/00036811.2023.2173183."},"date_updated":"2024-04-07T12:36:11Z","publication_status":"published","intvolume":" 103","year":"2023","title":"Refined regularity analysis for a Keller-Segel-consumption system involving signal-dependent motilities","author":[{"full_name":"Li, Genglin","last_name":"Li","first_name":"Genglin"},{"full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael"}],"publication_identifier":{"issn":["0003-6811","1563-504X"]},"doi":"10.1080/00036811.2023.2173183","language":[{"iso":"eng"}],"publication":"Applicable Analysis","issue":"1","type":"journal_article","keyword":["Applied Mathematics","Analysis"],"date_created":"2024-04-07T12:32:55Z"},{"status":"public","page":"103-138","publisher":"World Scientific Pub Co Pte Ltd","_id":"53328","user_id":"31496","volume":33,"citation":{"ama":"Tao Y, Winkler M. Small-signal solutions to a nonlocal cross-diffusion model for interaction of scroungers with rapidly diffusing foragers. Mathematical Models and Methods in Applied Sciences. 2023;33(01):103-138. doi:10.1142/s0218202523500045","bibtex":"@article{Tao_Winkler_2023, title={Small-signal solutions to a nonlocal cross-diffusion model for interaction of scroungers with rapidly diffusing foragers}, volume={33}, DOI={10.1142/s0218202523500045}, number={01}, journal={Mathematical Models and Methods in Applied Sciences}, publisher={World Scientific Pub Co Pte Ltd}, author={Tao, Youshan and Winkler, Michael}, year={2023}, pages={103–138} }","mla":"Tao, Youshan, and Michael Winkler. “Small-Signal Solutions to a Nonlocal Cross-Diffusion Model for Interaction of Scroungers with Rapidly Diffusing Foragers.” Mathematical Models and Methods in Applied Sciences, vol. 33, no. 01, World Scientific Pub Co Pte Ltd, 2023, pp. 103–38, doi:10.1142/s0218202523500045.","chicago":"Tao, Youshan, and Michael Winkler. “Small-Signal Solutions to a Nonlocal Cross-Diffusion Model for Interaction of Scroungers with Rapidly Diffusing Foragers.” Mathematical Models and Methods in Applied Sciences 33, no. 01 (2023): 103–38. https://doi.org/10.1142/s0218202523500045.","short":"Y. Tao, M. Winkler, Mathematical Models and Methods in Applied Sciences 33 (2023) 103–138.","apa":"Tao, Y., & Winkler, M. (2023). Small-signal solutions to a nonlocal cross-diffusion model for interaction of scroungers with rapidly diffusing foragers. Mathematical Models and Methods in Applied Sciences, 33(01), 103–138. https://doi.org/10.1142/s0218202523500045","ieee":"Y. Tao and M. Winkler, “Small-signal solutions to a nonlocal cross-diffusion model for interaction of scroungers with rapidly diffusing foragers,” Mathematical Models and Methods in Applied Sciences, vol. 33, no. 01, pp. 103–138, 2023, doi: 10.1142/s0218202523500045."},"year":"2023","title":"Small-signal solutions to a nonlocal cross-diffusion model for interaction of scroungers with rapidly diffusing foragers","author":[{"full_name":"Tao, Youshan","first_name":"Youshan","last_name":"Tao"},{"full_name":"Winkler, Michael","first_name":"Michael","last_name":"Winkler"}],"publication_identifier":{"issn":["0218-2025","1793-6314"]},"publication_status":"published","date_updated":"2024-04-07T12:43:17Z","intvolume":" 33","language":[{"iso":"eng"}],"doi":"10.1142/s0218202523500045","publication":"Mathematical Models and Methods in Applied Sciences","issue":"01","abstract":[{"text":" As a simplified version of a three-component taxis cascade model accounting for different migration strategies of two population groups in search of food, a two-component nonlocal nutrient taxis system is considered in a two-dimensional bounded convex domain with smooth boundary. For any given conveniently regular and biologically meaningful initial data, smallness conditions on the prescribed resource growth and on the initial nutrient signal concentration are identified which ensure the global existence of a global classical solution to the corresponding no-flux initial-boundary value problem. Moreover, under additional assumptions on the food production source these solutions are shown to be bounded, and to stabilize toward semi-trivial equilibria in the large time limit, respectively. ","lang":"eng"}],"date_created":"2024-04-07T12:43:13Z","type":"journal_article","keyword":["Applied Mathematics","Modeling and Simulation"]},{"citation":{"ama":"Ahn J, Winkler M. A critical exponent for blow-up in a two-dimensional chemotaxis-consumption system. Calculus of Variations and Partial Differential Equations. 2023;62(6). doi:10.1007/s00526-023-02523-5","bibtex":"@article{Ahn_Winkler_2023, title={A critical exponent for blow-up in a two-dimensional chemotaxis-consumption system}, volume={62}, DOI={10.1007/s00526-023-02523-5}, number={6180}, journal={Calculus of Variations and Partial Differential Equations}, publisher={Springer Science and Business Media LLC}, author={Ahn, Jaewook and Winkler, Michael}, year={2023} }","mla":"Ahn, Jaewook, and Michael Winkler. “A Critical Exponent for Blow-up in a Two-Dimensional Chemotaxis-Consumption System.” Calculus of Variations and Partial Differential Equations, vol. 62, no. 6, 180, Springer Science and Business Media LLC, 2023, doi:10.1007/s00526-023-02523-5.","short":"J. Ahn, M. Winkler, Calculus of Variations and Partial Differential Equations 62 (2023).","chicago":"Ahn, Jaewook, and Michael Winkler. “A Critical Exponent for Blow-up in a Two-Dimensional Chemotaxis-Consumption System.” Calculus of Variations and Partial Differential Equations 62, no. 6 (2023). https://doi.org/10.1007/s00526-023-02523-5.","apa":"Ahn, J., & Winkler, M. (2023). A critical exponent for blow-up in a two-dimensional chemotaxis-consumption system. Calculus of Variations and Partial Differential Equations, 62(6), Article 180. https://doi.org/10.1007/s00526-023-02523-5","ieee":"J. Ahn and M. Winkler, “A critical exponent for blow-up in a two-dimensional chemotaxis-consumption system,” Calculus of Variations and Partial Differential Equations, vol. 62, no. 6, Art. no. 180, 2023, doi: 10.1007/s00526-023-02523-5."},"status":"public","user_id":"31496","volume":62,"_id":"53324","publisher":"Springer Science and Business Media LLC","publication":"Calculus of Variations and Partial Differential Equations","issue":"6","type":"journal_article","keyword":["Applied Mathematics","Analysis"],"date_created":"2024-04-07T12:40:02Z","date_updated":"2024-04-07T12:40:06Z","publication_status":"published","intvolume":" 62","year":"2023","title":"A critical exponent for blow-up in a two-dimensional chemotaxis-consumption system","author":[{"full_name":"Ahn, Jaewook","last_name":"Ahn","first_name":"Jaewook"},{"full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael"}],"publication_identifier":{"issn":["0944-2669","1432-0835"]},"doi":"10.1007/s00526-023-02523-5","article_number":"180","language":[{"iso":"eng"}]},{"doi":"10.1016/j.nonrwa.2022.103820","user_id":"31496","volume":71,"article_number":"103820","_id":"53329","publisher":"Elsevier BV","language":[{"iso":"eng"}],"date_updated":"2024-04-07T12:43:53Z","publication_status":"published","intvolume":" 71","year":"2023","title":"Analysis of a chemotaxis-SIS epidemic model with unbounded infection force","status":"public","author":[{"full_name":"Tao, Youshan","last_name":"Tao","first_name":"Youshan"},{"last_name":"Winkler","first_name":"Michael","full_name":"Winkler, Michael"}],"publication_identifier":{"issn":["1468-1218"]},"keyword":["Applied Mathematics","Computational Mathematics","General Economics","Econometrics and Finance","General Engineering","General Medicine","Analysis"],"type":"journal_article","date_created":"2024-04-07T12:43:49Z","publication":"Nonlinear Analysis: Real World Applications","citation":{"ieee":"Y. Tao and M. Winkler, “Analysis of a chemotaxis-SIS epidemic model with unbounded infection force,” Nonlinear Analysis: Real World Applications, vol. 71, Art. no. 103820, 2023, doi: 10.1016/j.nonrwa.2022.103820.","apa":"Tao, Y., & Winkler, M. (2023). Analysis of a chemotaxis-SIS epidemic model with unbounded infection force. Nonlinear Analysis: Real World Applications, 71, Article 103820. https://doi.org/10.1016/j.nonrwa.2022.103820","chicago":"Tao, Youshan, and Michael Winkler. “Analysis of a Chemotaxis-SIS Epidemic Model with Unbounded Infection Force.” Nonlinear Analysis: Real World Applications 71 (2023). https://doi.org/10.1016/j.nonrwa.2022.103820.","short":"Y. Tao, M. Winkler, Nonlinear Analysis: Real World Applications 71 (2023).","mla":"Tao, Youshan, and Michael Winkler. “Analysis of a Chemotaxis-SIS Epidemic Model with Unbounded Infection Force.” Nonlinear Analysis: Real World Applications, vol. 71, 103820, Elsevier BV, 2023, doi:10.1016/j.nonrwa.2022.103820.","bibtex":"@article{Tao_Winkler_2023, title={Analysis of a chemotaxis-SIS epidemic model with unbounded infection force}, volume={71}, DOI={10.1016/j.nonrwa.2022.103820}, number={103820}, journal={Nonlinear Analysis: Real World Applications}, publisher={Elsevier BV}, author={Tao, Youshan and Winkler, Michael}, year={2023} }","ama":"Tao Y, Winkler M. Analysis of a chemotaxis-SIS epidemic model with unbounded infection force. Nonlinear Analysis: Real World Applications. 2023;71. doi:10.1016/j.nonrwa.2022.103820"}},{"publication":"Communications in Mathematical Sciences","issue":"2","type":"journal_article","keyword":["Applied Mathematics","General Mathematics"],"date_created":"2024-04-07T12:41:49Z","intvolume":" 21","publication_status":"published","date_updated":"2024-04-07T12:41:54Z","publication_identifier":{"issn":["1539-6746","1945-0796"]},"author":[{"first_name":"Genglin","last_name":"Li","full_name":"Li, Genglin"},{"full_name":"Winkler, Michael","first_name":"Michael","last_name":"Winkler"}],"year":"2023","title":"Relaxation in a Keller-Segel-consumption system involving signal-dependent motilities","doi":"10.4310/cms.2023.v21.n2.a1","language":[{"iso":"eng"}],"citation":{"bibtex":"@article{Li_Winkler_2023, title={Relaxation in a Keller-Segel-consumption system involving signal-dependent motilities}, volume={21}, DOI={10.4310/cms.2023.v21.n2.a1}, number={2}, journal={Communications in Mathematical Sciences}, publisher={International Press of Boston}, author={Li, Genglin and Winkler, Michael}, year={2023}, pages={299–322} }","ama":"Li G, Winkler M. Relaxation in a Keller-Segel-consumption system involving signal-dependent motilities. Communications in Mathematical Sciences. 2023;21(2):299-322. doi:10.4310/cms.2023.v21.n2.a1","mla":"Li, Genglin, and Michael Winkler. “Relaxation in a Keller-Segel-Consumption System Involving Signal-Dependent Motilities.” Communications in Mathematical Sciences, vol. 21, no. 2, International Press of Boston, 2023, pp. 299–322, doi:10.4310/cms.2023.v21.n2.a1.","short":"G. Li, M. Winkler, Communications in Mathematical Sciences 21 (2023) 299–322.","chicago":"Li, Genglin, and Michael Winkler. “Relaxation in a Keller-Segel-Consumption System Involving Signal-Dependent Motilities.” Communications in Mathematical Sciences 21, no. 2 (2023): 299–322. https://doi.org/10.4310/cms.2023.v21.n2.a1.","ieee":"G. Li and M. Winkler, “Relaxation in a Keller-Segel-consumption system involving signal-dependent motilities,” Communications in Mathematical Sciences, vol. 21, no. 2, pp. 299–322, 2023, doi: 10.4310/cms.2023.v21.n2.a1.","apa":"Li, G., & Winkler, M. (2023). Relaxation in a Keller-Segel-consumption system involving signal-dependent motilities. Communications in Mathematical Sciences, 21(2), 299–322. https://doi.org/10.4310/cms.2023.v21.n2.a1"},"status":"public","volume":21,"user_id":"31496","publisher":"International Press of Boston","_id":"53326","page":"299-322"},{"doi":"10.1515/math-2022-0578","language":[{"iso":"eng"}],"intvolume":" 21","date_updated":"2024-04-07T12:54:34Z","publication_status":"published","author":[{"full_name":"Winkler, Michael","first_name":"Michael","last_name":"Winkler"}],"publication_identifier":{"issn":["2391-5455"]},"year":"2023","title":"Classical solutions to Cauchy problems for parabolic–elliptic systems of Keller-Segel type","keyword":["General Mathematics"],"type":"journal_article","date_created":"2024-04-07T12:54:31Z","abstract":[{"lang":"eng","text":"Abstract\r\n The Cauchy problem in \r\n \r\n \r\n \r\n \r\n \r\n R\r\n \r\n \r\n n\r\n \r\n \r\n \r\n {{\\mathbb{R}}}^{n}\r\n \r\n , \r\n \r\n \r\n \r\n n\r\n ≥\r\n 2\r\n \r\n n\\ge 2\r\n \r\n , for \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 u\r\n \r\n \r\n t\r\n \r\n \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 u\r\n S\r\n ⋅\r\n \r\n ∇\r\n \r\n v\r\n \r\n )\r\n \r\n ,\r\n \r\n \r\n \r\n \r\n 0\r\n =\r\n Δ\r\n v\r\n +\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 ⋆\r\n \r\n )\r\n \r\n \r\n \r\n \r\n \r\n \\begin{array}{r}\\left\\{\\phantom{\\rule[-1.25em]{}{0ex}}\\begin{array}{l}{u}_{t}=\\Delta u-\\nabla \\cdot \\left(uS\\cdot \\nabla v),\\\\ 0=\\Delta v+u,\\end{array}\\right.\\hspace{2.0em}\\hspace{2.0em}\\hspace{2.0em}\\left(\\star )\\end{array}\r\n \r\n is considered for general matrices \r\n \r\n \r\n \r\n S\r\n ∈\r\n \r\n \r\n R\r\n \r\n \r\n n\r\n ×\r\n n\r\n \r\n \r\n \r\n S\\in {{\\mathbb{R}}}^{n\\times n}\r\n \r\n . A theory of local-in-time classical existence and extensibility is developed in a framework that differs from those considered in large parts of the literature by involving bounded classical solutions. Specifically, it is shown that for all non-negative initial data belonging to \r\n \r\n \r\n \r\n BUC\r\n \r\n (\r\n \r\n \r\n \r\n R\r\n \r\n \r\n n\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 p\r\n \r\n \r\n \r\n (\r\n \r\n \r\n \r\n R\r\n \r\n \r\n n\r\n \r\n \r\n \r\n )\r\n \r\n \r\n {\\rm{BUC}}\\left({{\\mathbb{R}}}^{n})\\cap {L}^{p}\\left({{\\mathbb{R}}}^{n})\r\n \r\n with some \r\n \r\n \r\n \r\n p\r\n ∈\r\n \r\n [\r\n \r\n 1\r\n ,\r\n n\r\n \r\n )\r\n \r\n \r\n p\\in \\left[1,n)\r\n \r\n , there exist \r\n \r\n \r\n \r\n \r\n \r\n T\r\n \r\n \r\n max\r\n \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 {T}_{\\max }\\in \\left(0,\\infty ]\r\n \r\n and a uniquely determined \r\n \r\n \r\n \r\n u\r\n ∈\r\n \r\n \r\n C\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 0\r\n ,\r\n \r\n \r\n T\r\n \r\n \r\n max\r\n \r\n \r\n \r\n )\r\n \r\n ;\r\n \r\n BUC\r\n \r\n (\r\n \r\n \r\n \r\n R\r\n \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 \r\n \r\n C\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 0\r\n ,\r\n \r\n \r\n T\r\n \r\n \r\n max\r\n \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 p\r\n \r\n \r\n \r\n (\r\n \r\n \r\n \r\n R\r\n \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 \r\n \r\n C\r\n \r\n \r\n ∞\r\n \r\n \r\n \r\n (\r\n \r\n \r\n \r\n R\r\n \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 \r\n T\r\n \r\n \r\n max\r\n \r\n \r\n \r\n )\r\n \r\n \r\n )\r\n \r\n \r\n u\\in {C}^{0}\\left(\\left[0,{T}_{\\max });\\hspace{0.33em}{\\rm{BUC}}\\left({{\\mathbb{R}}}^{n}))\\cap {C}^{0}\\left(\\left[0,{T}_{\\max });\\hspace{0.33em}{L}^{p}\\left({{\\mathbb{R}}}^{n}))\\cap {C}^{\\infty }\\left({{\\mathbb{R}}}^{n}\\times \\left(0,{T}_{\\max }))\r\n \r\n such that with \r\n \r\n \r\n \r\n v\r\n ≔\r\n Γ\r\n ⋆\r\n u\r\n \r\n v:= \\Gamma \\star u\r\n \r\n , and with \r\n \r\n \r\n \r\n Γ\r\n \r\n \\Gamma \r\n \r\n denoting the Newtonian kernel on \r\n \r\n \r\n \r\n \r\n \r\n R\r\n \r\n \r\n n\r\n \r\n \r\n \r\n {{\\mathbb{R}}}^{n}\r\n \r\n , the pair \r\n \r\n \r\n \r\n \r\n (\r\n \r\n u\r\n ,\r\n v\r\n \r\n )\r\n \r\n \r\n \\left(u,v)\r\n \r\n forms a classical solution of (\r\n \r\n \r\n \r\n ⋆\r\n \r\n \\star \r\n \r\n ) in \r\n \r\n \r\n \r\n \r\n \r\n R\r\n \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 \r\n T\r\n \r\n \r\n max\r\n \r\n \r\n \r\n )\r\n \r\n \r\n {{\\mathbb{R}}}^{n}\\times \\left(0,{T}_{\\max })\r\n \r\n , which has the property that \r\n \r\n \r\n \r\n \r\n if\r\n \r\n \r\n \r\n \r\n T\r\n \r\n \r\n max\r\n \r\n \r\n <\r\n ∞\r\n ,\r\n \r\n \r\n \r\n then both\r\n \r\n \r\n \r\n \r\n \r\n limsup\r\n \r\n \r\n t\r\n ↗\r\n \r\n \r\n T\r\n \r\n \r\n max\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 ,\r\n t\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 \r\n \r\n (\r\n \r\n \r\n \r\n R\r\n \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 \r\n \r\n and\r\n \r\n \r\n \r\n \r\n limsup\r\n \r\n \r\n t\r\n ↗\r\n \r\n \r\n T\r\n \r\n \r\n max\r\n \r\n \r\n \r\n \r\n \r\n \r\n ‖\r\n \r\n ∇\r\n \r\n v\r\n \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 \r\n \r\n L\r\n \r\n \r\n ∞\r\n \r\n \r\n \r\n (\r\n \r\n \r\n \r\n R\r\n \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 .\r\n \r\n \\hspace{0.1em}\\text{if}\\hspace{0.1em}\\hspace{0.33em}{T}_{\\max }\\lt \\infty ,\\hspace{1.0em}\\hspace{0.1em}\\text{then both}\\hspace{0.1em}\\hspace{0.33em}\\mathop{\\mathrm{limsup}}\\limits_{t\\nearrow {T}_{\\max }}\\Vert u\\left(\\cdot ,t){\\Vert }_{{L}^{\\infty }\\left({{\\mathbb{R}}}^{n})}=\\infty \\hspace{1.0em}\\hspace{0.1em}\\text{and}\\hspace{0.1em}\\hspace{1.0em}\\mathop{\\mathrm{limsup}}\\limits_{t\\nearrow {T}_{\\max }}\\Vert \\nabla v\\left(\\cdot ,t){\\Vert }_{{L}^{\\infty }\\left({{\\mathbb{R}}}^{n})}=\\infty .\r\n \r\n An exemplary application of this provides a result on global classical solvability in cases when \r\n \r\n \r\n \r\n ∣\r\n S\r\n +\r\n 1\r\n ∣\r\n \r\n | S+{\\bf{1}}| \r\n \r\n is sufficiently small, where \r\n \r\n \r\n \r\n 1\r\n =\r\n diag\r\n \r\n \r\n (\r\n \r\n 1\r\n ,\r\n \r\n …\r\n \r\n ,\r\n 1\r\n \r\n )\r\n \r\n \r\n {\\bf{1}}={\\rm{diag}}\\hspace{0.33em}\\left(1,\\ldots ,1)\r\n \r\n ."}],"publication":"Open Mathematics","issue":"1","volume":21,"user_id":"31496","_id":"53343","publisher":"Walter de Gruyter GmbH","status":"public","citation":{"ieee":"M. Winkler, “Classical solutions to Cauchy problems for parabolic–elliptic systems of Keller-Segel type,” Open Mathematics, vol. 21, no. 1, 2023, doi: 10.1515/math-2022-0578.","apa":"Winkler, M. (2023). Classical solutions to Cauchy problems for parabolic–elliptic systems of Keller-Segel type. Open Mathematics, 21(1). https://doi.org/10.1515/math-2022-0578","chicago":"Winkler, Michael. “Classical Solutions to Cauchy Problems for Parabolic–Elliptic Systems of Keller-Segel Type.” Open Mathematics 21, no. 1 (2023). https://doi.org/10.1515/math-2022-0578.","short":"M. Winkler, Open Mathematics 21 (2023).","mla":"Winkler, Michael. “Classical Solutions to Cauchy Problems for Parabolic–Elliptic Systems of Keller-Segel Type.” Open Mathematics, vol. 21, no. 1, Walter de Gruyter GmbH, 2023, doi:10.1515/math-2022-0578.","bibtex":"@article{Winkler_2023, title={Classical solutions to Cauchy problems for parabolic–elliptic systems of Keller-Segel type}, volume={21}, DOI={10.1515/math-2022-0578}, number={1}, journal={Open Mathematics}, publisher={Walter de Gruyter GmbH}, author={Winkler, Michael}, year={2023} }","ama":"Winkler M. Classical solutions to Cauchy problems for parabolic–elliptic systems of Keller-Segel type. Open Mathematics. 2023;21(1). doi:10.1515/math-2022-0578"}},{"user_id":"31496","volume":36,"page":"4438-4469","_id":"53345","publisher":"IOP Publishing","status":"public","citation":{"mla":"Winkler, Michael. “Stabilization despite Pervasive Strong Cross-Degeneracies in a Nonlinear Diffusion Model for Migration–Consumption Interaction.” Nonlinearity, vol. 36, no. 8, IOP Publishing, 2023, pp. 4438–69, doi:10.1088/1361-6544/ace22e.","ama":"Winkler M. Stabilization despite pervasive strong cross-degeneracies in a nonlinear diffusion model for migration–consumption interaction. Nonlinearity. 2023;36(8):4438-4469. doi:10.1088/1361-6544/ace22e","bibtex":"@article{Winkler_2023, title={Stabilization despite pervasive strong cross-degeneracies in a nonlinear diffusion model for migration–consumption interaction}, volume={36}, DOI={10.1088/1361-6544/ace22e}, number={8}, journal={Nonlinearity}, publisher={IOP Publishing}, author={Winkler, Michael}, year={2023}, pages={4438–4469} }","apa":"Winkler, M. (2023). Stabilization despite pervasive strong cross-degeneracies in a nonlinear diffusion model for migration–consumption interaction. Nonlinearity, 36(8), 4438–4469. https://doi.org/10.1088/1361-6544/ace22e","ieee":"M. Winkler, “Stabilization despite pervasive strong cross-degeneracies in a nonlinear diffusion model for migration–consumption interaction,” Nonlinearity, vol. 36, no. 8, pp. 4438–4469, 2023, doi: 10.1088/1361-6544/ace22e.","chicago":"Winkler, Michael. “Stabilization despite Pervasive Strong Cross-Degeneracies in a Nonlinear Diffusion Model for Migration–Consumption Interaction.” Nonlinearity 36, no. 8 (2023): 4438–69. https://doi.org/10.1088/1361-6544/ace22e.","short":"M. Winkler, Nonlinearity 36 (2023) 4438–4469."},"doi":"10.1088/1361-6544/ace22e","language":[{"iso":"eng"}],"publication_status":"published","date_updated":"2024-04-07T12:56:40Z","intvolume":" 36","title":"Stabilization despite pervasive strong cross-degeneracies in a nonlinear diffusion model for migration–consumption interaction","year":"2023","author":[{"full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael"}],"publication_identifier":{"issn":["0951-7715","1361-6544"]},"keyword":["Applied Mathematics","General Physics and Astronomy","Mathematical Physics","Statistical and Nonlinear Physics"],"type":"journal_article","date_created":"2024-04-07T12:56:35Z","abstract":[{"text":"AbstractA no-flux initial-boundary value problem forut=Δ(uϕ(v)),vt=Δv−uv,(⋆)is considered in smoothly bounded subdomains ofRnwithn⩾1and suitably regular initial data, whereφis assumed to reflect algebraic type cross-degeneracies by sharing essential features with0⩽ξ↦ξαfor someα⩾1. Based on the discovery of a gradient structure acting at regularity levels mild enough to be consistent with degeneracy-driven limitations of smoothness information, in this general setting it is shown that with some measurable limit profileu∞and some null setN⋆⊂(0,∞), a corresponding global generalized solution, known to exist according to recent literature, satisfiesρ(u(⋅,t))⇀⋆ρ(u∞)in L∞(Ω) and v(⋅,t)→0in Lp(Ω)for all p⩾1as(0,∞)∖N⋆∋t→∞, whereρ(ξ):=ξ2(ξ+1)2,ξ⩾0. In the particular case when eithern⩽2andα⩾1is arbitrary, orn⩾1andα∈[1,2], additional quantitative information on the deviation of trajectories from the initial data is derived. This is found to imply a lower estimate for the spatial oscillation of the respective first components throughout evolution, and moreover this is seen to entail that each of the uncountably many steady states(u⋆,0)of (⋆) is stable with respect to a suitably chosen norm topology.","lang":"eng"}],"issue":"8","publication":"Nonlinearity"},{"language":[{"iso":"eng"}],"doi":"10.1007/s41808-023-00230-y","author":[{"last_name":"Winkler","first_name":"Michael","full_name":"Winkler, Michael"}],"publication_identifier":{"issn":["2296-9020","2296-9039"]},"year":"2023","title":"Solutions to the Keller–Segel system with non-integrable behavior at spatial infinity","intvolume":" 9","publication_status":"published","date_updated":"2024-04-07T12:52:55Z","date_created":"2024-04-07T12:52:52Z","type":"journal_article","keyword":["Applied Mathematics","Numerical Analysis","Analysis"],"issue":"2","publication":"Journal of Elliptic and Parabolic Equations","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 is considered for the Keller–Segel system $$\\begin{aligned} \\left\\{ \\begin{array}{l}u_t = \\Delta u - \\nabla \\cdot (u\\nabla v), \\\\ 0 = \\Delta v + u, \\end{array} \\right. \\qquad \\qquad (\\star ) \\end{aligned}$$\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 Δ\r\n u\r\n -\r\n ∇\r\n ·\r\n \r\n (\r\n u\r\n ∇\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 0\r\n =\r\n Δ\r\n v\r\n +\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 )\r\n \r\n \r\n \r\n \r\n \r\n \r\n with a focus on a detailed description of behavior in the presence of nonnegative radially symmetric initial data $$u_0$$\r\n \r\n u\r\n 0\r\n \r\n with non-integrable behavior at spatial infinity. It is shown that if $$u_0$$\r\n \r\n u\r\n 0\r\n \r\n is continuous and bounded, then ($$\\star $$\r\n ⋆\r\n ) admits a local-in-time classical solution, whereas if $$u_0(x)\\rightarrow +\\infty $$\r\n \r\n \r\n u\r\n 0\r\n \r\n \r\n (\r\n x\r\n )\r\n \r\n →\r\n +\r\n ∞\r\n \r\n as $$|x|\\rightarrow \\infty $$\r\n \r\n |\r\n x\r\n |\r\n →\r\n ∞\r\n \r\n , then no such solution can be found. Furthermore, a collection of three sufficient criteria for either global existence or global nonexistence indicates that with respect to the occurrence of finite-time blow-up, spatial decay properties of an explicit singular steady state plays a critical role. In particular, this underlines that explosions in ($$\\star $$\r\n ⋆\r\n ) need not be enforced by initially high concentrations near finite points, but can be exclusively due to large tails.","lang":"eng"}],"publisher":"Springer Science and Business Media LLC","_id":"53341","page":"919-959","volume":9,"user_id":"31496","status":"public","citation":{"mla":"Winkler, Michael. “Solutions to the Keller–Segel System with Non-Integrable Behavior at Spatial Infinity.” Journal of Elliptic and Parabolic Equations, vol. 9, no. 2, Springer Science and Business Media LLC, 2023, pp. 919–59, doi:10.1007/s41808-023-00230-y.","ama":"Winkler M. Solutions to the Keller–Segel system with non-integrable behavior at spatial infinity. Journal of Elliptic and Parabolic Equations. 2023;9(2):919-959. doi:10.1007/s41808-023-00230-y","bibtex":"@article{Winkler_2023, title={Solutions to the Keller–Segel system with non-integrable behavior at spatial infinity}, volume={9}, DOI={10.1007/s41808-023-00230-y}, number={2}, journal={Journal of Elliptic and Parabolic Equations}, publisher={Springer Science and Business Media LLC}, author={Winkler, Michael}, year={2023}, pages={919–959} }","apa":"Winkler, M. (2023). Solutions to the Keller–Segel system with non-integrable behavior at spatial infinity. Journal of Elliptic and Parabolic Equations, 9(2), 919–959. https://doi.org/10.1007/s41808-023-00230-y","ieee":"M. Winkler, “Solutions to the Keller–Segel system with non-integrable behavior at spatial infinity,” Journal of Elliptic and Parabolic Equations, vol. 9, no. 2, pp. 919–959, 2023, doi: 10.1007/s41808-023-00230-y.","short":"M. Winkler, Journal of Elliptic and Parabolic Equations 9 (2023) 919–959.","chicago":"Winkler, Michael. “Solutions to the Keller–Segel System with Non-Integrable Behavior at Spatial Infinity.” Journal of Elliptic and Parabolic Equations 9, no. 2 (2023): 919–59. https://doi.org/10.1007/s41808-023-00230-y."}},{"volume":46,"user_id":"31496","publisher":"Wiley","_id":"53339","page":"15667-15683","status":"public","citation":{"short":"Y. Tian, M. Winkler, Mathematical Methods in the Applied Sciences 46 (2023) 15667–15683.","chicago":"Tian, Yu, and Michael Winkler. “Keller–Segel–Stokes Interaction Involving Signal‐dependent Motilities.” Mathematical Methods in the Applied Sciences 46, no. 14 (2023): 15667–83. https://doi.org/10.1002/mma.9419.","apa":"Tian, Y., & Winkler, M. (2023). Keller–Segel–Stokes interaction involving signal‐dependent motilities. Mathematical Methods in the Applied Sciences, 46(14), 15667–15683. https://doi.org/10.1002/mma.9419","ieee":"Y. Tian and M. Winkler, “Keller–Segel–Stokes interaction involving signal‐dependent motilities,” Mathematical Methods in the Applied Sciences, vol. 46, no. 14, pp. 15667–15683, 2023, doi: 10.1002/mma.9419.","ama":"Tian Y, Winkler M. Keller–Segel–Stokes interaction involving signal‐dependent motilities. Mathematical Methods in the Applied Sciences. 2023;46(14):15667-15683. doi:10.1002/mma.9419","bibtex":"@article{Tian_Winkler_2023, title={Keller–Segel–Stokes interaction involving signal‐dependent motilities}, volume={46}, DOI={10.1002/mma.9419}, number={14}, journal={Mathematical Methods in the Applied Sciences}, publisher={Wiley}, author={Tian, Yu and Winkler, Michael}, year={2023}, pages={15667–15683} }","mla":"Tian, Yu, and Michael Winkler. “Keller–Segel–Stokes Interaction Involving Signal‐dependent Motilities.” Mathematical Methods in the Applied Sciences, vol. 46, no. 14, Wiley, 2023, pp. 15667–83, doi:10.1002/mma.9419."},"doi":"10.1002/mma.9419","language":[{"iso":"eng"}],"intvolume":" 46","publication_status":"published","date_updated":"2024-04-07T12:51:31Z","author":[{"full_name":"Tian, Yu","last_name":"Tian","first_name":"Yu"},{"full_name":"Winkler, Michael","first_name":"Michael","last_name":"Winkler"}],"publication_identifier":{"issn":["0170-4214","1099-1476"]},"title":"Keller–Segel–Stokes interaction involving signal‐dependent motilities","year":"2023","type":"journal_article","keyword":["General Engineering","General Mathematics"],"date_created":"2024-04-07T12:51:27Z","abstract":[{"lang":"eng","text":"The chemotaxis‐Stokes system \r\n\r\n\r\nis considered along with homogeneous boundary conditions of no‐flux type for \r\n and \r\n, and of Dirichlet type for \r\n, in a smoothly bounded domain \r\n. Under the assumption that \r\n, that \r\n is bounded on each of the intervals \r\n with arbitrary \r\n, and that with some \r\n and \r\n, we have \r\n\r\n\r\nIt is shown that for any suitably regular initial data, an associated initial‐boundary value problem admits a global very weak solution."}],"issue":"14","publication":"Mathematical Methods in the Applied Sciences"},{"citation":{"mla":"Painter, Kevin J., and Michael Winkler. “Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities.” SIAM Journal on Applied Mathematics, vol. 83, no. 5, Society for Industrial & Applied Mathematics (SIAM), 2023, pp. 2096–117, doi:10.1137/22m1539393.","ama":"Painter KJ, Winkler M. Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities. SIAM Journal on Applied Mathematics. 2023;83(5):2096-2117. doi:10.1137/22m1539393","bibtex":"@article{Painter_Winkler_2023, title={Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities}, volume={83}, DOI={10.1137/22m1539393}, number={5}, journal={SIAM Journal on Applied Mathematics}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Painter, Kevin J. and Winkler, Michael}, year={2023}, pages={2096–2117} }","apa":"Painter, K. J., & Winkler, M. (2023). Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities. SIAM Journal on Applied Mathematics, 83(5), 2096–2117. https://doi.org/10.1137/22m1539393","ieee":"K. J. Painter and M. Winkler, “Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities,” SIAM Journal on Applied Mathematics, vol. 83, no. 5, pp. 2096–2117, 2023, doi: 10.1137/22m1539393.","short":"K.J. Painter, M. Winkler, SIAM Journal on Applied Mathematics 83 (2023) 2096–2117.","chicago":"Painter, Kevin J., and Michael Winkler. “Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities.” SIAM Journal on Applied Mathematics 83, no. 5 (2023): 2096–2117. https://doi.org/10.1137/22m1539393."},"volume":83,"user_id":"31496","_id":"53340","publisher":"Society for Industrial & Applied Mathematics (SIAM)","page":"2096-2117","status":"public","type":"journal_article","keyword":["Applied Mathematics"],"date_created":"2024-04-07T12:52:03Z","issue":"5","publication":"SIAM Journal on Applied Mathematics","doi":"10.1137/22m1539393","language":[{"iso":"eng"}],"intvolume":" 83","publication_status":"published","date_updated":"2024-04-07T12:52:06Z","publication_identifier":{"issn":["0036-1399","1095-712X"]},"author":[{"full_name":"Painter, Kevin J.","first_name":"Kevin J.","last_name":"Painter"},{"full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael"}],"year":"2023","title":"Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities"},{"publication_status":"published","date_updated":"2024-04-07T12:53:38Z","intvolume":" 374","year":"2023","title":"Avoiding critical mass phenomena by arbitrarily mild saturation of cross-diffusive fluxes in two-dimensional Keller-Segel-Navier-Stokes systems","status":"public","author":[{"full_name":"Winkler, Michael","first_name":"Michael","last_name":"Winkler"},{"first_name":"Tomomi","last_name":"Yokota","full_name":"Yokota, Tomomi"}],"publication_identifier":{"issn":["0022-0396"]},"user_id":"31496","doi":"10.1016/j.jde.2023.07.029","volume":374,"page":"1-28","_id":"53342","publisher":"Elsevier BV","language":[{"iso":"eng"}],"publication":"Journal of Differential Equations","citation":{"apa":"Winkler, M., & Yokota, T. (2023). Avoiding critical mass phenomena by arbitrarily mild saturation of cross-diffusive fluxes in two-dimensional Keller-Segel-Navier-Stokes systems. Journal of Differential Equations, 374, 1–28. https://doi.org/10.1016/j.jde.2023.07.029","ieee":"M. Winkler and T. Yokota, “Avoiding critical mass phenomena by arbitrarily mild saturation of cross-diffusive fluxes in two-dimensional Keller-Segel-Navier-Stokes systems,” Journal of Differential Equations, vol. 374, pp. 1–28, 2023, doi: 10.1016/j.jde.2023.07.029.","short":"M. Winkler, T. Yokota, Journal of Differential Equations 374 (2023) 1–28.","chicago":"Winkler, Michael, and Tomomi Yokota. “Avoiding Critical Mass Phenomena by Arbitrarily Mild Saturation of Cross-Diffusive Fluxes in Two-Dimensional Keller-Segel-Navier-Stokes Systems.” Journal of Differential Equations 374 (2023): 1–28. https://doi.org/10.1016/j.jde.2023.07.029.","mla":"Winkler, Michael, and Tomomi Yokota. “Avoiding Critical Mass Phenomena by Arbitrarily Mild Saturation of Cross-Diffusive Fluxes in Two-Dimensional Keller-Segel-Navier-Stokes Systems.” Journal of Differential Equations, vol. 374, Elsevier BV, 2023, pp. 1–28, doi:10.1016/j.jde.2023.07.029.","ama":"Winkler M, Yokota T. Avoiding critical mass phenomena by arbitrarily mild saturation of cross-diffusive fluxes in two-dimensional Keller-Segel-Navier-Stokes systems. Journal of Differential Equations. 2023;374:1-28. doi:10.1016/j.jde.2023.07.029","bibtex":"@article{Winkler_Yokota_2023, title={Avoiding critical mass phenomena by arbitrarily mild saturation of cross-diffusive fluxes in two-dimensional Keller-Segel-Navier-Stokes systems}, volume={374}, DOI={10.1016/j.jde.2023.07.029}, journal={Journal of Differential Equations}, publisher={Elsevier BV}, author={Winkler, Michael and Yokota, Tomomi}, year={2023}, pages={1–28} }"},"keyword":["Analysis","Applied Mathematics"],"type":"journal_article","date_created":"2024-04-07T12:53:32Z"},{"date_created":"2024-04-07T12:57:19Z","type":"journal_article","keyword":["Applied Mathematics","Analysis"],"issue":"11/12","publication":"Advances in Differential Equations","citation":{"bibtex":"@article{Winkler_2023, title={Absence of collapse into persistent Dirac-type singularities in a Keller-Segel-Navier-Stokes system involving local sensing}, volume={28}, DOI={10.57262/ade028-1112-921}, number={11/12}, journal={Advances in Differential Equations}, publisher={Khayyam Publishing, Inc}, author={Winkler, Michael}, year={2023} }","ama":"Winkler M. Absence of collapse into persistent Dirac-type singularities in a Keller-Segel-Navier-Stokes system involving local sensing. Advances in Differential Equations. 2023;28(11/12). doi:10.57262/ade028-1112-921","mla":"Winkler, Michael. “Absence of Collapse into Persistent Dirac-Type Singularities in a Keller-Segel-Navier-Stokes System Involving Local Sensing.” Advances in Differential Equations, vol. 28, no. 11/12, Khayyam Publishing, Inc, 2023, doi:10.57262/ade028-1112-921.","chicago":"Winkler, Michael. “Absence of Collapse into Persistent Dirac-Type Singularities in a Keller-Segel-Navier-Stokes System Involving Local Sensing.” Advances in Differential Equations 28, no. 11/12 (2023). https://doi.org/10.57262/ade028-1112-921.","short":"M. Winkler, Advances in Differential Equations 28 (2023).","ieee":"M. Winkler, “Absence of collapse into persistent Dirac-type singularities in a Keller-Segel-Navier-Stokes system involving local sensing,” Advances in Differential Equations, vol. 28, no. 11/12, 2023, doi: 10.57262/ade028-1112-921.","apa":"Winkler, M. (2023). Absence of collapse into persistent Dirac-type singularities in a Keller-Segel-Navier-Stokes system involving local sensing. Advances in Differential Equations, 28(11/12). https://doi.org/10.57262/ade028-1112-921"},"_id":"53346","publisher":"Khayyam Publishing, Inc","language":[{"iso":"eng"}],"doi":"10.57262/ade028-1112-921","user_id":"31496","volume":28,"title":"Absence of collapse into persistent Dirac-type singularities in a Keller-Segel-Navier-Stokes system involving local sensing","year":"2023","status":"public","publication_identifier":{"issn":["1079-9389"]},"author":[{"full_name":"Winkler, Michael","first_name":"Michael","last_name":"Winkler"}],"date_updated":"2024-04-07T12:57:23Z","publication_status":"published","intvolume":" 28"},{"doi":"10.1109/tfuzz.2022.3188875","language":[{"iso":"eng"}],"date_updated":"2024-04-15T13:15:07Z","publication_status":"published","intvolume":" 31","year":"2023","title":"A Credibility and Strategic Behavior Approach in Hesitant Multiple Criteria Decision-Making With Application to Sustainable Transportation","author":[{"full_name":"Santos-Arteaga, Francisco J.","last_name":"Santos-Arteaga","first_name":"Francisco J."},{"first_name":"Debora","last_name":"Di Caprio","full_name":"Di Caprio, Debora"},{"last_name":"Tavana","first_name":"Madjid","full_name":"Tavana, Madjid","id":"31858"},{"last_name":"Tena","first_name":"Emilio Cerda","full_name":"Tena, Emilio Cerda"}],"publication_identifier":{"issn":["1063-6706","1941-0034"]},"type":"journal_article","keyword":["Applied Mathematics","Artificial Intelligence","Computational Theory and Mathematics","Control and Systems Engineering"],"department":[{"_id":"277"}],"date_created":"2024-04-04T14:00:53Z","publication":"IEEE Transactions on Fuzzy Systems","issue":"2","user_id":"51811","volume":31,"page":"460-474","_id":"53229","publisher":"Institute of Electrical and Electronics Engineers (IEEE)","status":"public","citation":{"ieee":"F. J. Santos-Arteaga, D. Di Caprio, M. Tavana, and E. C. Tena, “A Credibility and Strategic Behavior Approach in Hesitant Multiple Criteria Decision-Making With Application to Sustainable Transportation,” IEEE Transactions on Fuzzy Systems, vol. 31, no. 2, pp. 460–474, 2023, doi: 10.1109/tfuzz.2022.3188875.","apa":"Santos-Arteaga, F. J., Di Caprio, D., Tavana, M., & Tena, E. C. (2023). A Credibility and Strategic Behavior Approach in Hesitant Multiple Criteria Decision-Making With Application to Sustainable Transportation. IEEE Transactions on Fuzzy Systems, 31(2), 460–474. https://doi.org/10.1109/tfuzz.2022.3188875","short":"F.J. Santos-Arteaga, D. Di Caprio, M. Tavana, E.C. Tena, IEEE Transactions on Fuzzy Systems 31 (2023) 460–474.","chicago":"Santos-Arteaga, Francisco J., Debora Di Caprio, Madjid Tavana, and Emilio Cerda Tena. “A Credibility and Strategic Behavior Approach in Hesitant Multiple Criteria Decision-Making With Application to Sustainable Transportation.” IEEE Transactions on Fuzzy Systems 31, no. 2 (2023): 460–74. https://doi.org/10.1109/tfuzz.2022.3188875.","mla":"Santos-Arteaga, Francisco J., et al. “A Credibility and Strategic Behavior Approach in Hesitant Multiple Criteria Decision-Making With Application to Sustainable Transportation.” IEEE Transactions on Fuzzy Systems, vol. 31, no. 2, Institute of Electrical and Electronics Engineers (IEEE), 2023, pp. 460–74, doi:10.1109/tfuzz.2022.3188875.","bibtex":"@article{Santos-Arteaga_Di Caprio_Tavana_Tena_2023, title={A Credibility and Strategic Behavior Approach in Hesitant Multiple Criteria Decision-Making With Application to Sustainable Transportation}, volume={31}, DOI={10.1109/tfuzz.2022.3188875}, number={2}, journal={IEEE Transactions on Fuzzy Systems}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Santos-Arteaga, Francisco J. and Di Caprio, Debora and Tavana, Madjid and Tena, Emilio Cerda}, year={2023}, pages={460–474} }","ama":"Santos-Arteaga FJ, Di Caprio D, Tavana M, Tena EC. A Credibility and Strategic Behavior Approach in Hesitant Multiple Criteria Decision-Making With Application to Sustainable Transportation. IEEE Transactions on Fuzzy Systems. 2023;31(2):460-474. doi:10.1109/tfuzz.2022.3188875"}},{"language":[{"iso":"eng"}],"_id":"53538","publisher":"Springer Science and Business Media LLC","doi":"10.1007/s13163-023-00476-z","user_id":"100325","author":[{"full_name":"Polychrou, G.","last_name":"Polychrou","first_name":"G."},{"first_name":"Efthymia","last_name":"Papageorgiou","full_name":"Papageorgiou, Efthymia","id":"100325"},{"full_name":"Fotiadis, A.","first_name":"A.","last_name":"Fotiadis"},{"full_name":"Daskaloyannis, C.","last_name":"Daskaloyannis","first_name":"C."}],"publication_identifier":{"issn":["1139-1138","1988-2807"]},"status":"public","year":"2023","title":"New examples of harmonic maps to the hyperbolic plane via Bäcklund transformation","date_updated":"2024-04-17T13:15:51Z","publication_status":"published","date_created":"2024-04-17T13:15:07Z","department":[{"_id":"555"}],"type":"journal_article","keyword":["General Mathematics"],"citation":{"mla":"Polychrou, G., et al. “New Examples of Harmonic Maps to the Hyperbolic Plane via Bäcklund Transformation.” Revista Matemática Complutense, Springer Science and Business Media LLC, 2023, doi:10.1007/s13163-023-00476-z.","bibtex":"@article{Polychrou_Papageorgiou_Fotiadis_Daskaloyannis_2023, title={New examples of harmonic maps to the hyperbolic plane via Bäcklund transformation}, DOI={10.1007/s13163-023-00476-z}, journal={Revista Matemática Complutense}, publisher={Springer Science and Business Media LLC}, author={Polychrou, G. and Papageorgiou, Efthymia and Fotiadis, A. and Daskaloyannis, C.}, year={2023} }","ama":"Polychrou G, Papageorgiou E, Fotiadis A, Daskaloyannis C. New examples of harmonic maps to the hyperbolic plane via Bäcklund transformation. Revista Matemática Complutense. Published online 2023. doi:10.1007/s13163-023-00476-z","ieee":"G. Polychrou, E. Papageorgiou, A. Fotiadis, and C. Daskaloyannis, “New examples of harmonic maps to the hyperbolic plane via Bäcklund transformation,” Revista Matemática Complutense, 2023, doi: 10.1007/s13163-023-00476-z.","apa":"Polychrou, G., Papageorgiou, E., Fotiadis, A., & Daskaloyannis, C. (2023). New examples of harmonic maps to the hyperbolic plane via Bäcklund transformation. Revista Matemática Complutense. https://doi.org/10.1007/s13163-023-00476-z","chicago":"Polychrou, G., Efthymia Papageorgiou, A. Fotiadis, and C. Daskaloyannis. “New Examples of Harmonic Maps to the Hyperbolic Plane via Bäcklund Transformation.” Revista Matemática Complutense, 2023. https://doi.org/10.1007/s13163-023-00476-z.","short":"G. Polychrou, E. Papageorgiou, A. Fotiadis, C. Daskaloyannis, Revista Matemática Complutense (2023)."},"publication":"Revista Matemática Complutense","abstract":[{"lang":"eng","text":"AbstractWe study harmonic maps from a subset of the complex plane to a subset of the hyperbolic plane. In Fotiadis and Daskaloyannis (Nonlinear Anal 214, 112546, 2022), harmonic maps are related to the sinh-Gordon equation and a Bäcklund transformation is introduced, which connects solutions of the sinh-Gordon and sine-Gordon equation. We develop this machinery in order to construct new harmonic maps to the hyperbolic plane."}]},{"has_accepted_license":"1","status":"public","ddc":["510","370"],"user_id":"37888","publisher":"Springer","_id":"45786","quality_controlled":"1","file_date_updated":"2023-07-13T09:40:02Z","citation":{"chicago":"Hoffmann, Max, and Rolf Biehler. “Implementing Profession Orientation as a Design Principle for Overcoming Klein’s Second Discontinuity – Preservice Teacher’s Perspectives on Interface Activities in the Context of a Geometry Course.” ZDM – Mathematics Education, 2023. https://doi.org/10.1007/s11858-023-01505-3.","short":"M. Hoffmann, R. Biehler, ZDM – Mathematics Education (2023).","ieee":"M. Hoffmann and R. Biehler, “Implementing profession orientation as a design principle for overcoming Klein’s second discontinuity – preservice teacher’s perspectives on interface activities in the context of a geometry course,” ZDM – Mathematics Education, 2023, doi: 10.1007/s11858-023-01505-3.","apa":"Hoffmann, M., & Biehler, R. (2023). Implementing profession orientation as a design principle for overcoming Klein’s second discontinuity – preservice teacher’s perspectives on interface activities in the context of a geometry course. ZDM – Mathematics Education. https://doi.org/10.1007/s11858-023-01505-3","bibtex":"@article{Hoffmann_Biehler_2023, title={Implementing profession orientation as a design principle for overcoming Klein’s second discontinuity – preservice teacher’s perspectives on interface activities in the context of a geometry course}, DOI={10.1007/s11858-023-01505-3}, journal={ZDM – Mathematics Education}, publisher={Springer}, author={Hoffmann, Max and Biehler, Rolf}, year={2023} }","ama":"Hoffmann M, Biehler R. Implementing profession orientation as a design principle for overcoming Klein’s second discontinuity – preservice teacher’s perspectives on interface activities in the context of a geometry course. ZDM – Mathematics Education. Published online 2023. doi:10.1007/s11858-023-01505-3","mla":"Hoffmann, Max, and Rolf Biehler. “Implementing Profession Orientation as a Design Principle for Overcoming Klein’s Second Discontinuity – Preservice Teacher’s Perspectives on Interface Activities in the Context of a Geometry Course.” ZDM – Mathematics Education, Springer, 2023, doi:10.1007/s11858-023-01505-3."},"oa":"1","date_updated":"2024-04-18T09:01:29Z","publication_status":"published","article_type":"original","year":"2023","title":"Implementing profession orientation as a design principle for overcoming Klein’s second discontinuity – preservice teacher’s perspectives on interface activities in the context of a geometry course","publication_identifier":{"issn":["1863-9690","1863-9704"]},"author":[{"full_name":"Hoffmann, Max","first_name":"Max","last_name":"Hoffmann","orcid":"0000-0002-6964-7123","id":"32202"},{"last_name":"Biehler","first_name":"Rolf","full_name":"Biehler, Rolf","id":"16274"}],"doi":"10.1007/s11858-023-01505-3","main_file_link":[{"open_access":"1","url":"https://link.springer.com/article/10.1007/s11858-023-01505-3"}],"language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"Intending to counteract Klein’s second discontinuity in teacher education, we explored and applied the innovation of “interface ePortfolio” in the context of a geometry course for preservice teachers (PSTs). The tool offers the possibility of implementing the design principle of profession orientation. In the article, we theoretically clarify what we understand by this principle and locate our innovative concept against this theoretical background. We empirically investigate the extent to which counteraction against the second discontinuity is successful by analyzing reflection texts created in the interface ePortfolio, focusing on PSTs’ perspectives. Our qualitative content analysis shows that most of them perceive the innovation as helpful in the intended sense and indicates that the course concept, in general, and the interface ePortfolio, in particular, have helped establish relevant links between the course content and their later work as teachers."}],"publication":"ZDM – Mathematics Education","keyword":["General Mathematics","Education"],"type":"journal_article","department":[{"_id":"643"}],"file":[{"creator":"maxh","date_created":"2023-07-13T09:40:02Z","date_updated":"2023-07-13T09:40:02Z","relation":"main_file","access_level":"closed","file_size":1460246,"file_name":"s11858-023-01505-3.pdf","content_type":"application/pdf","success":1,"file_id":"46041"}],"date_created":"2023-06-27T11:45:25Z"},{"publisher":"Springer Science and Business Media LLC","_id":"46569","language":[{"iso":"eng"}],"doi":"10.1007/s11858-023-01494-3","user_id":"99409","publication_identifier":{"issn":["1863-9690","1863-9704"]},"author":[{"full_name":"Schoenherr, Johanna","first_name":"Johanna","last_name":"Schoenherr"},{"full_name":"Schukajlow, Stanislaw","last_name":"Schukajlow","first_name":"Stanislaw"}],"year":"2023","status":"public","title":"Characterizing external visualization in mathematics education research: a scoping review","date_updated":"2024-04-30T13:43:22Z","publication_status":"published","date_created":"2023-08-17T10:11:45Z","department":[{"_id":"913"}],"keyword":["General Mathematics","Education"],"type":"journal_article","citation":{"mla":"Schoenherr, Johanna, and Stanislaw Schukajlow. “Characterizing External Visualization in Mathematics Education Research: A Scoping Review.” ZDM – Mathematics Education, Springer Science and Business Media LLC, 2023, doi:10.1007/s11858-023-01494-3.","bibtex":"@article{Schoenherr_Schukajlow_2023, title={Characterizing external visualization in mathematics education research: a scoping review}, DOI={10.1007/s11858-023-01494-3}, journal={ZDM – Mathematics Education}, publisher={Springer Science and Business Media LLC}, author={Schoenherr, Johanna and Schukajlow, Stanislaw}, year={2023} }","ama":"Schoenherr J, Schukajlow S. Characterizing external visualization in mathematics education research: a scoping review. ZDM – Mathematics Education. Published online 2023. doi:10.1007/s11858-023-01494-3","ieee":"J. Schoenherr and S. Schukajlow, “Characterizing external visualization in mathematics education research: a scoping review,” ZDM – Mathematics Education, 2023, doi: 10.1007/s11858-023-01494-3.","apa":"Schoenherr, J., & Schukajlow, S. (2023). Characterizing external visualization in mathematics education research: a scoping review. ZDM – Mathematics Education. https://doi.org/10.1007/s11858-023-01494-3","short":"J. Schoenherr, S. Schukajlow, ZDM – Mathematics Education (2023).","chicago":"Schoenherr, Johanna, and Stanislaw Schukajlow. “Characterizing External Visualization in Mathematics Education Research: A Scoping Review.” ZDM – Mathematics Education, 2023. https://doi.org/10.1007/s11858-023-01494-3."},"publication":"ZDM – Mathematics Education","abstract":[{"text":"AbstractExternal visualization (i.e., physically embodied visualization) is central to the teaching and learning of mathematics. As external visualization is an important part of mathematics at all levels of education, it is diverse, and research on external visualization has become a wide and complex field. The aim of this scoping review is to characterize external visualizations in recent mathematics education research in order to develop a common ground and guide future research. A qualitative content analysis of the full texts of 130 studies published between 2018 and 2022 applied a deductive-inductive coding procedure to assess four dimensions: visualization product or process, type of visualization, media, and purpose. The analysis revealed different types of external visualizations including visualizations with physical resemblance ranging from pictorial to abstract visualizations as well as three types of visualizations with structural resemblance: length, area, and relational visualizations. Future research should include measures of visualization products or processes to help explain the demands and affordances that different types of visualizations present to learners and teachers.","lang":"eng"}]}]