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Loddenkemper, Expert Systems with Applications 234 (2023).","mla":"Vieluf, Solveig, et al. “Developing a Deep Canonical Correlation-Based Technique for Seizure Prediction.” Expert Systems with Applications, vol. 234, 120986, Elsevier BV, 2023, doi:10.1016/j.eswa.2023.120986.","chicago":"Vieluf, Solveig, Tanuj Hasija, Maurice Kuschel, Claus Reinsberger, and Tobias Loddenkemper. “Developing a Deep Canonical Correlation-Based Technique for Seizure Prediction.” Expert Systems with Applications 234 (2023). https://doi.org/10.1016/j.eswa.2023.120986.","ieee":"S. Vieluf, T. Hasija, M. Kuschel, C. Reinsberger, and T. Loddenkemper, “Developing a deep canonical correlation-based technique for seizure prediction,” Expert Systems with Applications, vol. 234, Art. no. 120986, 2023, doi: 10.1016/j.eswa.2023.120986.","ama":"Vieluf S, Hasija T, Kuschel M, Reinsberger C, Loddenkemper T. Developing a deep canonical correlation-based technique for seizure prediction. Expert Systems with Applications. 2023;234. doi:10.1016/j.eswa.2023.120986"},"publication_identifier":{"issn":["0957-4174"]},"publication_status":"published","title":"Developing a deep canonical correlation-based technique for seizure prediction","doi":"10.1016/j.eswa.2023.120986","publisher":"Elsevier BV","date_updated":"2024-04-05T14:49:56Z","volume":234,"author":[{"last_name":"Vieluf","full_name":"Vieluf, Solveig","first_name":"Solveig"},{"first_name":"Tanuj","last_name":"Hasija","id":"43497","full_name":"Hasija, Tanuj"},{"last_name":"Kuschel","id":"56070","full_name":"Kuschel, Maurice","first_name":"Maurice"},{"first_name":"Claus","last_name":"Reinsberger","full_name":"Reinsberger, Claus","id":"48978"},{"last_name":"Loddenkemper","full_name":"Loddenkemper, Tobias","first_name":"Tobias"}],"date_created":"2024-04-05T14:37:06Z"},{"author":[{"first_name":"Maurice","last_name":"Kuschel","full_name":"Kuschel, Maurice","id":"56070"},{"full_name":"Marrinan, Timothy","last_name":"Marrinan","first_name":"Timothy"},{"last_name":"Hasija","id":"43497","full_name":"Hasija, Tanuj","first_name":"Tanuj"}],"date_created":"2024-04-05T14:39:36Z","publisher":"IEEE","date_updated":"2024-04-05T14:50:06Z","doi":"10.1109/mlsp55844.2023.10285937","title":"Geodesic-Based Relaxation For Deep Canonical Correlation Analysis","publication_status":"published","citation":{"apa":"Kuschel, M., Marrinan, T., & Hasija, T. 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Marrinan, and T. Hasija, “Geodesic-Based Relaxation For Deep Canonical Correlation Analysis,” 2023, doi: 10.1109/mlsp55844.2023.10285937.","chicago":"Kuschel, Maurice, Timothy Marrinan, and Tanuj Hasija. “Geodesic-Based Relaxation For Deep Canonical Correlation Analysis.” In 2023 IEEE 33rd International Workshop on Machine Learning for Signal Processing (MLSP). IEEE, 2023. https://doi.org/10.1109/mlsp55844.2023.10285937.","ama":"Kuschel M, Marrinan T, Hasija T. Geodesic-Based Relaxation For Deep Canonical Correlation Analysis. In: 2023 IEEE 33rd International Workshop on Machine Learning for Signal Processing (MLSP). IEEE; 2023. doi:10.1109/mlsp55844.2023.10285937"},"year":"2023","department":[{"_id":"263"}],"user_id":"56070","_id":"53303","language":[{"iso":"eng"}],"publication":"2023 IEEE 33rd International Workshop on Machine Learning for Signal Processing (MLSP)","type":"conference","status":"public"},{"language":[{"iso":"eng"}],"_id":"53310","department":[{"_id":"52"}],"user_id":"66","status":"public","publication":"2023 IEEE 14th International Symposium on Diagnostics for Electrical Machines, Power Electronics and Drives (SDEMPED)","type":"conference","title":"Online system identification and excitation for thermal monitoring of electric machines using machine learning and model predictive control","doi":"10.1109/sdemped54949.2023.10271427","publisher":"IEEE","date_updated":"2024-04-06T14:00:07Z","author":[{"first_name":"Emebet Gebeyehu","last_name":"Gedlu","id":"77572","full_name":"Gedlu, Emebet Gebeyehu"},{"first_name":"Oliver","last_name":"Wallscheid","orcid":"https://orcid.org/0000-0001-9362-8777","id":"11291","full_name":"Wallscheid, Oliver"},{"id":"66","full_name":"Böcker, Joachim","last_name":"Böcker","orcid":"0000-0002-8480-7295","first_name":"Joachim"},{"last_name":"Nelles","full_name":"Nelles, Oliver","first_name":"Oliver"}],"date_created":"2024-04-06T13:55:29Z","year":"2023","citation":{"short":"E.G. Gedlu, O. Wallscheid, J. Böcker, O. Nelles, in: 2023 IEEE 14th International Symposium on Diagnostics for Electrical Machines, Power Electronics and Drives (SDEMPED), IEEE, 2023.","mla":"Gedlu, Emebet Gebeyehu, et al. “Online System Identification and Excitation for Thermal Monitoring of Electric Machines Using Machine Learning and Model Predictive Control.” 2023 IEEE 14th International Symposium on Diagnostics for Electrical Machines, Power Electronics and Drives (SDEMPED), IEEE, 2023, doi:10.1109/sdemped54949.2023.10271427.","bibtex":"@inproceedings{Gedlu_Wallscheid_Böcker_Nelles_2023, title={Online system identification and excitation for thermal monitoring of electric machines using machine learning and model predictive control}, DOI={10.1109/sdemped54949.2023.10271427}, booktitle={2023 IEEE 14th International Symposium on Diagnostics for Electrical Machines, Power Electronics and Drives (SDEMPED)}, publisher={IEEE}, author={Gedlu, Emebet Gebeyehu and Wallscheid, Oliver and Böcker, Joachim and Nelles, Oliver}, year={2023} }","apa":"Gedlu, E. G., Wallscheid, O., Böcker, J., & Nelles, O. (2023). Online system identification and excitation for thermal monitoring of electric machines using machine learning and model predictive control. 2023 IEEE 14th International Symposium on Diagnostics for Electrical Machines, Power Electronics and Drives (SDEMPED). https://doi.org/10.1109/sdemped54949.2023.10271427","ama":"Gedlu EG, Wallscheid O, Böcker J, Nelles O. Online system identification and excitation for thermal monitoring of electric machines using machine learning and model predictive control. In: 2023 IEEE 14th International Symposium on Diagnostics for Electrical Machines, Power Electronics and Drives (SDEMPED). IEEE; 2023. doi:10.1109/sdemped54949.2023.10271427","chicago":"Gedlu, Emebet Gebeyehu, Oliver Wallscheid, Joachim Böcker, and Oliver Nelles. “Online System Identification and Excitation for Thermal Monitoring of Electric Machines Using Machine Learning and Model Predictive Control.” In 2023 IEEE 14th International Symposium on Diagnostics for Electrical Machines, Power Electronics and Drives (SDEMPED). IEEE, 2023. https://doi.org/10.1109/sdemped54949.2023.10271427.","ieee":"E. G. Gedlu, O. Wallscheid, J. Böcker, and O. Nelles, “Online system identification and excitation for thermal monitoring of electric machines using machine learning and model predictive control,” 2023, doi: 10.1109/sdemped54949.2023.10271427."},"publication_status":"published"},{"type":"journal_article","publication":"Evolution Equations and Control Theory","status":"public","user_id":"31496","_id":"53317","language":[{"iso":"eng"}],"keyword":["Applied Mathematics","Control and Optimization","Modeling and Simulation"],"issue":"6","publication_status":"published","publication_identifier":{"issn":["2163-2480"]},"citation":{"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.","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.","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","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","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."},"intvolume":" 12","page":"1676-1687","year":"2023","date_created":"2024-04-07T12:30:25Z","author":[{"first_name":"Youshan","full_name":"Tao, Youshan","last_name":"Tao"},{"last_name":"Winkler","full_name":"Winkler, Michael","first_name":"Michael"}],"volume":12,"date_updated":"2024-04-07T12:36:17Z","publisher":"American Institute of Mathematical Sciences (AIMS)","doi":"10.3934/eect.2023031","title":"Global smooth solutions in a three-dimensional cross-diffusive SIS epidemic model with saturated taxis at large densities"},{"type":"journal_article","publication":"Annales de l'Institut Henri Poincaré C, Analyse non linéaire","status":"public","user_id":"31496","_id":"53320","language":[{"iso":"eng"}],"keyword":["Mathematical Physics","Analysis","Applied Mathematics"],"publication_status":"published","publication_identifier":{"issn":["0294-1449","1873-1430"]},"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","short":"M. Winkler, Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire (2023).","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.","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} }","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.","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.","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"},"year":"2023","author":[{"full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael"}],"date_created":"2024-04-07T12:34:35Z","publisher":"European Mathematical Society - EMS - Publishing House GmbH","date_updated":"2024-04-07T12:36:00Z","doi":"10.4171/aihpc/73","title":"A quantitative strong parabolic maximum principle and application to a taxis-type migration–consumption model involving signal-dependent degenerate diffusion"},{"doi":"10.1080/00036811.2023.2173183","title":"Refined regularity analysis for a Keller-Segel-consumption system involving signal-dependent motilities","volume":103,"author":[{"first_name":"Genglin","full_name":"Li, Genglin","last_name":"Li"},{"last_name":"Winkler","full_name":"Winkler, Michael","first_name":"Michael"}],"date_created":"2024-04-07T12:32:55Z","publisher":"Informa UK Limited","date_updated":"2024-04-07T12:36:11Z","page":"45-64","intvolume":" 103","citation":{"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","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.","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.","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","short":"G. Li, M. Winkler, Applicable Analysis 103 (2023) 45–64.","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} }","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."},"year":"2023","issue":"1","publication_identifier":{"issn":["0003-6811","1563-504X"]},"publication_status":"published","language":[{"iso":"eng"}],"keyword":["Applied Mathematics","Analysis"],"user_id":"31496","_id":"53318","status":"public","publication":"Applicable Analysis","type":"journal_article"},{"status":"public","type":"journal_article","_id":"53328","user_id":"31496","page":"103-138","intvolume":" 33","citation":{"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.","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.","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","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","short":"Y. Tao, M. Winkler, Mathematical Models and Methods in Applied Sciences 33 (2023) 103–138.","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."},"publication_identifier":{"issn":["0218-2025","1793-6314"]},"publication_status":"published","doi":"10.1142/s0218202523500045","date_updated":"2024-04-07T12:43:17Z","volume":33,"author":[{"first_name":"Youshan","full_name":"Tao, Youshan","last_name":"Tao"},{"first_name":"Michael","full_name":"Winkler, Michael","last_name":"Winkler"}],"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"}],"publication":"Mathematical Models and Methods in Applied Sciences","keyword":["Applied Mathematics","Modeling and Simulation"],"language":[{"iso":"eng"}],"year":"2023","issue":"01","title":"Small-signal solutions to a nonlocal cross-diffusion model for interaction of scroungers with rapidly diffusing foragers","publisher":"World Scientific Pub Co Pte Ltd","date_created":"2024-04-07T12:43:13Z"},{"status":"public","publication":"Calculus of Variations and Partial Differential Equations","type":"journal_article","keyword":["Applied Mathematics","Analysis"],"article_number":"180","language":[{"iso":"eng"}],"_id":"53324","user_id":"31496","year":"2023","intvolume":" 62","citation":{"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.","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} }","short":"J. Ahn, M. Winkler, Calculus of Variations and Partial Differential Equations 62 (2023).","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","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.","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.","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"},"publication_identifier":{"issn":["0944-2669","1432-0835"]},"publication_status":"published","issue":"6","title":"A critical exponent for blow-up in a two-dimensional chemotaxis-consumption system","doi":"10.1007/s00526-023-02523-5","publisher":"Springer Science and Business Media LLC","date_updated":"2024-04-07T12:40:06Z","volume":62,"date_created":"2024-04-07T12:40:02Z","author":[{"first_name":"Jaewook","last_name":"Ahn","full_name":"Ahn, Jaewook"},{"full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael"}]},{"publication":"Nonlinear Analysis: Real World Applications","type":"journal_article","status":"public","user_id":"31496","_id":"53329","language":[{"iso":"eng"}],"keyword":["Applied Mathematics","Computational Mathematics","General Economics","Econometrics and Finance","General Engineering","General Medicine","Analysis"],"article_number":"103820","publication_identifier":{"issn":["1468-1218"]},"publication_status":"published","intvolume":" 71","citation":{"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","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.","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.","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.","short":"Y. Tao, M. Winkler, Nonlinear Analysis: Real World Applications 71 (2023).","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} }","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"},"year":"2023","volume":71,"date_created":"2024-04-07T12:43:49Z","author":[{"last_name":"Tao","full_name":"Tao, Youshan","first_name":"Youshan"},{"first_name":"Michael","full_name":"Winkler, Michael","last_name":"Winkler"}],"date_updated":"2024-04-07T12:43:53Z","publisher":"Elsevier BV","doi":"10.1016/j.nonrwa.2022.103820","title":"Analysis of a chemotaxis-SIS epidemic model with unbounded infection force"},{"_id":"53326","user_id":"31496","keyword":["Applied Mathematics","General Mathematics"],"language":[{"iso":"eng"}],"publication":"Communications in Mathematical Sciences","type":"journal_article","status":"public","publisher":"International Press of Boston","date_updated":"2024-04-07T12:41:54Z","volume":21,"author":[{"first_name":"Genglin","full_name":"Li, Genglin","last_name":"Li"},{"first_name":"Michael","last_name":"Winkler","full_name":"Winkler, Michael"}],"date_created":"2024-04-07T12:41:49Z","title":"Relaxation in a Keller-Segel-consumption system involving signal-dependent motilities","doi":"10.4310/cms.2023.v21.n2.a1","publication_identifier":{"issn":["1539-6746","1945-0796"]},"publication_status":"published","issue":"2","year":"2023","intvolume":" 21","page":"299-322","citation":{"short":"G. Li, M. Winkler, Communications in Mathematical Sciences 21 (2023) 299–322.","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.","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} }","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","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","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."}},{"citation":{"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.","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.","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","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} }","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"},"intvolume":" 21","year":"2023","issue":"1","publication_status":"published","publication_identifier":{"issn":["2391-5455"]},"doi":"10.1515/math-2022-0578","title":"Classical solutions to Cauchy problems for parabolic–elliptic systems of Keller-Segel type","author":[{"first_name":"Michael","full_name":"Winkler, Michael","last_name":"Winkler"}],"date_created":"2024-04-07T12:54:31Z","volume":21,"publisher":"Walter de Gruyter GmbH","date_updated":"2024-04-07T12:54:34Z","status":"public","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 ."}],"type":"journal_article","publication":"Open Mathematics","language":[{"iso":"eng"}],"keyword":["General Mathematics"],"user_id":"31496","_id":"53343"}]