[{"title":"Protein–protein interactions in solutions of monoclonal antibodies probed by the dependence of the high-frequency viscosity on temperature and concentration","year":"2023","author":[{"last_name":"Rott","first_name":"Emily","full_name":"Rott, Emily"},{"id":"117722","full_name":"Leppin, Christian","first_name":"Christian","last_name":"Leppin"},{"full_name":"Diederichs, Tim","last_name":"Diederichs","first_name":"Tim"},{"last_name":"Garidel","first_name":"Patrick","full_name":"Garidel, Patrick"},{"full_name":"Johannsmann, Diethelm","last_name":"Johannsmann","first_name":"Diethelm"}],"publication_identifier":{"issn":["0003-2654","1364-5528"]},"publication_status":"published","date_updated":"2025-12-18T17:38:31Z","intvolume":" 148","language":[{"iso":"eng"}],"doi":"10.1039/d3an00076a","issue":"8","publication":"The Analyst","abstract":[{"text":"\r\n A QCM-D probes the temperature- and concentration-dependent complex high-frequency viscosity and provides information on protein-protein interactions in solutions of monoclonal antibodies.","lang":"eng"}],"date_created":"2025-12-18T17:06:08Z","type":"journal_article","status":"public","page":"1887-1897","publisher":"Royal Society of Chemistry (RSC)","_id":"63231","user_id":"117722","volume":148,"citation":{"apa":"Rott, E., Leppin, C., Diederichs, T., Garidel, P., & Johannsmann, D. (2023). Protein–protein interactions in solutions of monoclonal antibodies probed by the dependence of the high-frequency viscosity on temperature and concentration. The Analyst, 148(8), 1887–1897. https://doi.org/10.1039/d3an00076a","ieee":"E. Rott, C. Leppin, T. Diederichs, P. Garidel, and D. Johannsmann, “Protein–protein interactions in solutions of monoclonal antibodies probed by the dependence of the high-frequency viscosity on temperature and concentration,” The Analyst, vol. 148, no. 8, pp. 1887–1897, 2023, doi: 10.1039/d3an00076a.","short":"E. Rott, C. Leppin, T. Diederichs, P. Garidel, D. Johannsmann, The Analyst 148 (2023) 1887–1897.","chicago":"Rott, Emily, Christian Leppin, Tim Diederichs, Patrick Garidel, and Diethelm Johannsmann. “Protein–Protein Interactions in Solutions of Monoclonal Antibodies Probed by the Dependence of the High-Frequency Viscosity on Temperature and Concentration.” The Analyst 148, no. 8 (2023): 1887–97. https://doi.org/10.1039/d3an00076a.","mla":"Rott, Emily, et al. “Protein–Protein Interactions in Solutions of Monoclonal Antibodies Probed by the Dependence of the High-Frequency Viscosity on Temperature and Concentration.” The Analyst, vol. 148, no. 8, Royal Society of Chemistry (RSC), 2023, pp. 1887–97, doi:10.1039/d3an00076a.","ama":"Rott E, Leppin C, Diederichs T, Garidel P, Johannsmann D. Protein–protein interactions in solutions of monoclonal antibodies probed by the dependence of the high-frequency viscosity on temperature and concentration. The Analyst. 2023;148(8):1887-1897. doi:10.1039/d3an00076a","bibtex":"@article{Rott_Leppin_Diederichs_Garidel_Johannsmann_2023, title={Protein–protein interactions in solutions of monoclonal antibodies probed by the dependence of the high-frequency viscosity on temperature and concentration}, volume={148}, DOI={10.1039/d3an00076a}, number={8}, journal={The Analyst}, publisher={Royal Society of Chemistry (RSC)}, author={Rott, Emily and Leppin, Christian and Diederichs, Tim and Garidel, Patrick and Johannsmann, Diethelm}, year={2023}, pages={1887–1897} }"},"quality_controlled":"1"},{"status":"public","publisher":"Wiley","_id":"63228","volume":6,"user_id":"117722","citation":{"apa":"Johannsmann, D., Leppin, C., & Langhoff, A. (2023). Stiffness of Contacts between Adsorbed Particles and the Surface of a QCM‐D Inferred from the Adsorption Kinetics and a Frequency‐Domain Lattice Boltzmann Simulation. Advanced Theory and Simulations, 6(11), Article 2300190. https://doi.org/10.1002/adts.202300190","ieee":"D. Johannsmann, C. Leppin, and A. Langhoff, “Stiffness of Contacts between Adsorbed Particles and the Surface of a QCM‐D Inferred from the Adsorption Kinetics and a Frequency‐Domain Lattice Boltzmann Simulation,” Advanced Theory and Simulations, vol. 6, no. 11, Art. no. 2300190, 2023, doi: 10.1002/adts.202300190.","chicago":"Johannsmann, Diethelm, Christian Leppin, and Arne Langhoff. “Stiffness of Contacts between Adsorbed Particles and the Surface of a QCM‐D Inferred from the Adsorption Kinetics and a Frequency‐Domain Lattice Boltzmann Simulation.” Advanced Theory and Simulations 6, no. 11 (2023). https://doi.org/10.1002/adts.202300190.","short":"D. Johannsmann, C. Leppin, A. Langhoff, Advanced Theory and Simulations 6 (2023).","mla":"Johannsmann, Diethelm, et al. “Stiffness of Contacts between Adsorbed Particles and the Surface of a QCM‐D Inferred from the Adsorption Kinetics and a Frequency‐Domain Lattice Boltzmann Simulation.” Advanced Theory and Simulations, vol. 6, no. 11, 2300190, Wiley, 2023, doi:10.1002/adts.202300190.","ama":"Johannsmann D, Leppin C, Langhoff A. Stiffness of Contacts between Adsorbed Particles and the Surface of a QCM‐D Inferred from the Adsorption Kinetics and a Frequency‐Domain Lattice Boltzmann Simulation. Advanced Theory and Simulations. 2023;6(11). doi:10.1002/adts.202300190","bibtex":"@article{Johannsmann_Leppin_Langhoff_2023, title={Stiffness of Contacts between Adsorbed Particles and the Surface of a QCM‐D Inferred from the Adsorption Kinetics and a Frequency‐Domain Lattice Boltzmann Simulation}, volume={6}, DOI={10.1002/adts.202300190}, number={112300190}, journal={Advanced Theory and Simulations}, publisher={Wiley}, author={Johannsmann, Diethelm and Leppin, Christian and Langhoff, Arne}, year={2023} }"},"quality_controlled":"1","publication_identifier":{"issn":["2513-0390","2513-0390"]},"author":[{"full_name":"Johannsmann, Diethelm","last_name":"Johannsmann","first_name":"Diethelm"},{"id":"117722","first_name":"Christian","last_name":"Leppin","full_name":"Leppin, Christian"},{"full_name":"Langhoff, Arne","last_name":"Langhoff","first_name":"Arne"}],"title":"Stiffness of Contacts between Adsorbed Particles and the Surface of a QCM‐D Inferred from the Adsorption Kinetics and a Frequency‐Domain Lattice Boltzmann Simulation","year":"2023","intvolume":" 6","article_type":"original","date_updated":"2025-12-18T17:41:08Z","publication_status":"published","language":[{"iso":"eng"}],"article_number":"2300190","doi":"10.1002/adts.202300190","issue":"11","publication":"Advanced Theory and Simulations","abstract":[{"text":"AbstractA simulation based on the frequency‐domain lattice Boltzmann method (FreqD‐LBM) is employed to predict the shifts of resonance frequency, Δf, and half bandwidth, ΔΓ, of a quartz crystal microbalance with dissipation monitoring (QCM‐D) induced by the adsorption of rigid spheres to the resonator surface. The comparison with the experimental values of Δf and ΔΓ allows to estimate the stiffness of the contacts between the spheres and the resonator surface. The contact stiffness is of interest in contact mechanics, but also in sensing because it depends on the properties of thin films situated between the resonator surface and the sphere. The simulation differs from previous implementations of FreqD‐LBM insofar, as the material inside the particles is not included in the FreqD‐LBM algorithm. Rather, the particle surface is configured to be an oscillating boundary. The amplitude of the particles' motions (displacement and rotation) is governed by the force balance at the surface of the particle. Because the contact stiffness enters this balance, it can be derived from experimental values of Δf and ΔΓ. The simulation reproduces experiments by the Krakow group. For sufficiently small spheres, a contact stiffness can be derived from the comparison of the simulation with the experiment.","lang":"eng"}],"extern":"1","date_created":"2025-12-18T17:03:12Z","type":"journal_article"},{"quality_controlled":"1","citation":{"ieee":"D. Johannsmann, A. Langhoff, C. Leppin, I. Reviakine, and A. M. C. Maan, “Effect of Noise on Determining Ultrathin-Film Parameters from QCM-D Data with the Viscoelastic Model,” Sensors, vol. 23, no. 3, Art. no. 1348, 2023, doi: 10.3390/s23031348.","apa":"Johannsmann, D., Langhoff, A., Leppin, C., Reviakine, I., & Maan, A. M. C. (2023). Effect of Noise on Determining Ultrathin-Film Parameters from QCM-D Data with the Viscoelastic Model. Sensors, 23(3), Article 1348. https://doi.org/10.3390/s23031348","chicago":"Johannsmann, Diethelm, Arne Langhoff, Christian Leppin, Ilya Reviakine, and Anna M. C. Maan. “Effect of Noise on Determining Ultrathin-Film Parameters from QCM-D Data with the Viscoelastic Model.” Sensors 23, no. 3 (2023). https://doi.org/10.3390/s23031348.","short":"D. Johannsmann, A. Langhoff, C. Leppin, I. Reviakine, A.M.C. Maan, Sensors 23 (2023).","mla":"Johannsmann, Diethelm, et al. “Effect of Noise on Determining Ultrathin-Film Parameters from QCM-D Data with the Viscoelastic Model.” Sensors, vol. 23, no. 3, 1348, MDPI AG, 2023, doi:10.3390/s23031348.","bibtex":"@article{Johannsmann_Langhoff_Leppin_Reviakine_Maan_2023, title={Effect of Noise on Determining Ultrathin-Film Parameters from QCM-D Data with the Viscoelastic Model}, volume={23}, DOI={10.3390/s23031348}, number={31348}, journal={Sensors}, publisher={MDPI AG}, author={Johannsmann, Diethelm and Langhoff, Arne and Leppin, Christian and Reviakine, Ilya and Maan, Anna M. C.}, year={2023} }","ama":"Johannsmann D, Langhoff A, Leppin C, Reviakine I, Maan AMC. Effect of Noise on Determining Ultrathin-Film Parameters from QCM-D Data with the Viscoelastic Model. Sensors. 2023;23(3). doi:10.3390/s23031348"},"user_id":"117722","volume":23,"publisher":"MDPI AG","_id":"63230","status":"public","type":"journal_article","date_created":"2025-12-18T17:05:00Z","abstract":[{"lang":"eng","text":"Quartz crystal microbalance with dissipation monitoring (QCM-D) is a well-established technique for studying soft films. It can provide gravimetric as well as nongravimetric information about a film, such as its thickness and mechanical properties. The interpretation of sets of overtone-normalized frequency shifts, ∆f/n, and overtone-normalized shifts in half-bandwidth, ΔΓ/n, provided by QCM-D relies on a model that, in general, contains five independent parameters that are needed to describe film thickness and frequency-dependent viscoelastic properties. Here, we examine how noise inherent in experimental data affects the determination of these parameters. There are certain conditions where noise prevents the reliable determination of film thickness and the loss tangent. On the other hand, we show that there are conditions where it is possible to determine all five parameters. We relate these conditions to the mathematical properties of the model in terms of simple conceptual diagrams that can help users understand the model’s behavior. Finally, we present new open source software for QCM-D data analysis written in Python, PyQTM."}],"extern":"1","publication":"Sensors","issue":"3","doi":"10.3390/s23031348","article_number":"1348","language":[{"iso":"eng"}],"date_updated":"2025-12-18T17:39:52Z","publication_status":"published","intvolume":" 23","title":"Effect of Noise on Determining Ultrathin-Film Parameters from QCM-D Data with the Viscoelastic Model","year":"2023","publication_identifier":{"issn":["1424-8220"]},"author":[{"full_name":"Johannsmann, Diethelm","last_name":"Johannsmann","first_name":"Diethelm"},{"full_name":"Langhoff, Arne","last_name":"Langhoff","first_name":"Arne"},{"id":"117722","full_name":"Leppin, Christian","first_name":"Christian","last_name":"Leppin"},{"full_name":"Reviakine, Ilya","last_name":"Reviakine","first_name":"Ilya"},{"last_name":"Maan","first_name":"Anna M. C.","full_name":"Maan, Anna M. C."}]},{"citation":{"bibtex":"@article{Johannsmann_Petri_Leppin_Langhoff_Ibrahim_2023, title={Particle fouling at hot reactor walls monitored In situ with a QCM-D and modeled with the frequency-domain lattice Boltzmann method}, volume={45}, DOI={10.1016/j.rinp.2023.106219}, number={106219}, journal={Results in Physics}, publisher={Elsevier BV}, author={Johannsmann, Diethelm and Petri, Judith and Leppin, Christian and Langhoff, Arne and Ibrahim, Hozan}, year={2023} }","ama":"Johannsmann D, Petri J, Leppin C, Langhoff A, Ibrahim H. Particle fouling at hot reactor walls monitored In situ with a QCM-D and modeled with the frequency-domain lattice Boltzmann method. Results in Physics. 2023;45. doi:10.1016/j.rinp.2023.106219","mla":"Johannsmann, Diethelm, et al. “Particle Fouling at Hot Reactor Walls Monitored In Situ with a QCM-D and Modeled with the Frequency-Domain Lattice Boltzmann Method.” Results in Physics, vol. 45, 106219, Elsevier BV, 2023, doi:10.1016/j.rinp.2023.106219.","chicago":"Johannsmann, Diethelm, Judith Petri, Christian Leppin, Arne Langhoff, and Hozan Ibrahim. “Particle Fouling at Hot Reactor Walls Monitored In Situ with a QCM-D and Modeled with the Frequency-Domain Lattice Boltzmann Method.” Results in Physics 45 (2023). https://doi.org/10.1016/j.rinp.2023.106219.","short":"D. Johannsmann, J. Petri, C. Leppin, A. Langhoff, H. Ibrahim, Results in Physics 45 (2023).","ieee":"D. Johannsmann, J. Petri, C. Leppin, A. Langhoff, and H. Ibrahim, “Particle fouling at hot reactor walls monitored In situ with a QCM-D and modeled with the frequency-domain lattice Boltzmann method,” Results in Physics, vol. 45, Art. no. 106219, 2023, doi: 10.1016/j.rinp.2023.106219.","apa":"Johannsmann, D., Petri, J., Leppin, C., Langhoff, A., & Ibrahim, H. (2023). Particle fouling at hot reactor walls monitored In situ with a QCM-D and modeled with the frequency-domain lattice Boltzmann method. Results in Physics, 45, Article 106219. https://doi.org/10.1016/j.rinp.2023.106219"},"publication":"Results in Physics","extern":"1","date_created":"2025-12-18T17:04:13Z","type":"journal_article","author":[{"full_name":"Johannsmann, Diethelm","last_name":"Johannsmann","first_name":"Diethelm"},{"full_name":"Petri, Judith","last_name":"Petri","first_name":"Judith"},{"full_name":"Leppin, Christian","first_name":"Christian","last_name":"Leppin","id":"117722"},{"full_name":"Langhoff, Arne","first_name":"Arne","last_name":"Langhoff"},{"full_name":"Ibrahim, Hozan","first_name":"Hozan","last_name":"Ibrahim"}],"publication_identifier":{"issn":["2211-3797"]},"year":"2023","status":"public","title":"Particle fouling at hot reactor walls monitored In situ with a QCM-D and modeled with the frequency-domain lattice Boltzmann method","intvolume":" 45","publication_status":"published","date_updated":"2025-12-18T17:40:25Z","_id":"63229","language":[{"iso":"eng"}],"publisher":"Elsevier BV","article_number":"106219","volume":45,"user_id":"117722","doi":"10.1016/j.rinp.2023.106219"},{"year":"2023","title":"Absence of collapse into persistent Dirac-type singularities in a Keller-Segel-Navier-Stokes system involving local sensing","status":"public","publication_identifier":{"issn":["1079-9389"]},"author":[{"full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael","id":"31496"}],"publication_status":"published","date_updated":"2025-12-18T20:07:12Z","intvolume":" 28","_id":"63285","language":[{"iso":"eng"}],"publisher":"Khayyam Publishing, Inc","user_id":"31496","doi":"10.57262/ade028-1112-921","volume":28,"issue":"11/12","publication":"Advances in Differential Equations","citation":{"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.","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","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} }","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","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.","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)."},"date_created":"2025-12-18T19:18:31Z","type":"journal_article"},{"date_created":"2025-12-18T19:19:35Z","type":"journal_article","issue":"1","publication":"Open Mathematics","abstract":[{"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 .","lang":"eng"}],"article_number":"20220578","language":[{"iso":"eng"}],"doi":"10.1515/math-2022-0578","title":"Classical solutions to Cauchy problems for parabolic–elliptic systems of Keller-Segel type","year":"2023","author":[{"id":"31496","last_name":"Winkler","first_name":"Michael","full_name":"Winkler, Michael"}],"publication_identifier":{"issn":["2391-5455"]},"date_updated":"2025-12-18T20:07:34Z","publication_status":"published","intvolume":" 21","citation":{"short":"M. Winkler, Open Mathematics 21 (2023).","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, Art. no. 20220578, 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), Article 20220578. https://doi.org/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={120220578}, 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","mla":"Winkler, Michael. “Classical Solutions to Cauchy Problems for Parabolic–Elliptic Systems of Keller-Segel Type.” Open Mathematics, vol. 21, no. 1, 20220578, Walter de Gruyter GmbH, 2023, doi:10.1515/math-2022-0578."},"_id":"63288","publisher":"Walter de Gruyter GmbH","user_id":"31496","volume":21,"status":"public"},{"citation":{"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","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.","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.","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","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.","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} }"},"status":"public","volume":9,"user_id":"31496","_id":"63287","publisher":"Springer Science and Business Media LLC","page":"919-959","abstract":[{"lang":"eng","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."}],"issue":"2","publication":"Journal of Elliptic and Parabolic Equations","type":"journal_article","date_created":"2025-12-18T19:19:13Z","intvolume":" 9","date_updated":"2025-12-18T20:07:25Z","publication_status":"published","publication_identifier":{"issn":["2296-9020","2296-9039"]},"author":[{"full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael","id":"31496"}],"year":"2023","title":"Solutions to the Keller–Segel system with non-integrable behavior at spatial infinity","doi":"10.1007/s41808-023-00230-y","language":[{"iso":"eng"}]},{"intvolume":" 374","date_updated":"2025-12-18T20:07:42Z","publication_status":"published","author":[{"id":"31496","full_name":"Winkler, Michael","first_name":"Michael","last_name":"Winkler"},{"last_name":"Yokota","first_name":"Tomomi","full_name":"Yokota, Tomomi"}],"publication_identifier":{"issn":["0022-0396"]},"status":"public","title":"Avoiding critical mass phenomena by arbitrarily mild saturation of cross-diffusive fluxes in two-dimensional Keller-Segel-Navier-Stokes systems","year":"2023","volume":374,"doi":"10.1016/j.jde.2023.07.029","user_id":"31496","_id":"63289","language":[{"iso":"eng"}],"publisher":"Elsevier BV","page":"1-28","citation":{"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.","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","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.","short":"M. Winkler, T. Yokota, Journal of Differential Equations 374 (2023) 1–28.","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.","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} }","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"},"publication":"Journal of Differential Equations","type":"journal_article","date_created":"2025-12-18T19:19:57Z"},{"volume":33,"user_id":"31496","_id":"63271","publisher":"World Scientific Pub Co Pte Ltd","page":"103-138","status":"public","citation":{"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.","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","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.","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} }","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","short":"Y. Tao, M. Winkler, Mathematical Models and Methods in Applied Sciences 33 (2023) 103–138.","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."},"doi":"10.1142/s0218202523500045","language":[{"iso":"eng"}],"intvolume":" 33","publication_status":"published","date_updated":"2025-12-18T20:10:55Z","author":[{"full_name":"Tao, Youshan","first_name":"Youshan","last_name":"Tao"},{"id":"31496","full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael"}],"publication_identifier":{"issn":["0218-2025","1793-6314"]},"title":"Small-signal solutions to a nonlocal cross-diffusion model for interaction of scroungers with rapidly diffusing foragers","year":"2023","type":"journal_article","date_created":"2025-12-18T19:12:35Z","abstract":[{"lang":"eng","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. "}],"issue":"01","publication":"Mathematical Models and Methods in Applied Sciences"},{"type":"journal_article","date_created":"2025-12-18T19:10:55Z","citation":{"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.","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","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} }","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","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."},"issue":"6","publication":"Calculus of Variations and Partial Differential Equations","volume":62,"user_id":"31496","doi":"10.1007/s00526-023-02523-5","publisher":"Springer Science and Business Media LLC","_id":"63267","language":[{"iso":"eng"}],"article_number":"180","intvolume":" 62","publication_status":"published","date_updated":"2025-12-18T20:10:21Z","author":[{"full_name":"Ahn, Jaewook","first_name":"Jaewook","last_name":"Ahn"},{"last_name":"Winkler","first_name":"Michael","full_name":"Winkler, Michael","id":"31496"}],"publication_identifier":{"issn":["0944-2669","1432-0835"]},"year":"2023","status":"public","title":"A critical exponent for blow-up in a two-dimensional chemotaxis-consumption system"},{"type":"journal_article","date_created":"2025-12-18T19:12:01Z","citation":{"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} }","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","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","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.","short":"G. Li, M. Winkler, Communications in Mathematical Sciences 21 (2023) 299–322."},"issue":"2","publication":"Communications in Mathematical Sciences","volume":21,"user_id":"31496","doi":"10.4310/cms.2023.v21.n2.a1","_id":"63270","publisher":"International Press of Boston","language":[{"iso":"eng"}],"page":"299-322","intvolume":" 21","publication_status":"published","date_updated":"2025-12-18T20:10:48Z","author":[{"last_name":"Li","first_name":"Genglin","full_name":"Li, Genglin"},{"full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael","id":"31496"}],"publication_identifier":{"issn":["1539-6746","1945-0796"]},"title":"Relaxation in a Keller-Segel-consumption system involving signal-dependent motilities","status":"public","year":"2023"},{"type":"journal_article","date_created":"2025-12-18T19:13:40Z","publication":"Nonlinear Analysis: Real World Applications","citation":{"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} }","short":"Y. Tao, M. Winkler, Nonlinear Analysis: Real World Applications 71 (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","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.","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"},"user_id":"31496","doi":"10.1016/j.nonrwa.2022.103820","volume":71,"article_number":"103820","_id":"63273","publisher":"Elsevier BV","language":[{"iso":"eng"}],"publication_status":"published","date_updated":"2025-12-18T20:11:09Z","intvolume":" 71","status":"public","year":"2023","title":"Analysis of a chemotaxis-SIS epidemic model with unbounded infection force","author":[{"full_name":"Tao, Youshan","last_name":"Tao","first_name":"Youshan"},{"full_name":"Winkler, Michael","first_name":"Michael","last_name":"Winkler","id":"31496"}],"publication_identifier":{"issn":["1468-1218"]}},{"language":[{"iso":"eng"}],"doi":"10.1088/1361-6544/ace22e","publication_identifier":{"issn":["0951-7715","1361-6544"]},"author":[{"id":"31496","last_name":"Winkler","first_name":"Michael","full_name":"Winkler, Michael"}],"year":"2023","title":"Stabilization despite pervasive strong cross-degeneracies in a nonlinear diffusion model for migration–consumption interaction","intvolume":" 36","publication_status":"published","date_updated":"2025-12-18T20:12:06Z","date_created":"2025-12-18T19:17:01Z","type":"journal_article","publication":"Nonlinearity","issue":"8","abstract":[{"lang":"eng","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."}],"_id":"63281","publisher":"IOP Publishing","page":"4438-4469","volume":36,"user_id":"31496","status":"public","citation":{"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.","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","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.","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.","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} }","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"}},{"language":[{"iso":"eng"}],"doi":"10.1002/mma.9419","year":"2023","title":"Keller–Segel–Stokes interaction involving signal‐dependent motilities","publication_identifier":{"issn":["0170-4214","1099-1476"]},"author":[{"full_name":"Tian, Yu","last_name":"Tian","first_name":"Yu"},{"full_name":"Winkler, Michael","first_name":"Michael","last_name":"Winkler","id":"31496"}],"publication_status":"published","date_updated":"2025-12-18T20:11:29Z","intvolume":" 46","date_created":"2025-12-18T19:15:06Z","type":"journal_article","issue":"14","publication":"Mathematical Methods in the Applied Sciences","abstract":[{"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.","lang":"eng"}],"page":"15667-15683","publisher":"Wiley","_id":"63276","user_id":"31496","volume":46,"status":"public","citation":{"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.","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} }","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","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.","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","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.","short":"Y. Tian, M. Winkler, Mathematical Methods in the Applied Sciences 46 (2023) 15667–15683."}},{"publisher":"American Institute of Mathematical Sciences (AIMS)","_id":"63275","language":[{"iso":"eng"}],"page":"1676-1687","volume":12,"user_id":"31496","doi":"10.3934/eect.2023031","author":[{"first_name":"Youshan","last_name":"Tao","full_name":"Tao, Youshan"},{"last_name":"Winkler","first_name":"Michael","full_name":"Winkler, Michael","id":"31496"}],"publication_identifier":{"issn":["2163-2480"]},"status":"public","title":"Global smooth solutions in a three-dimensional cross-diffusive SIS epidemic model with saturated taxis at large densities","year":"2023","intvolume":" 12","publication_status":"published","date_updated":"2025-12-18T20:11:23Z","date_created":"2025-12-18T19:14:46Z","type":"journal_article","citation":{"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","short":"Y. Tao, M. Winkler, Evolution Equations and Control Theory 12 (2023) 1676–1687.","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.","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."},"publication":"Evolution Equations and Control Theory","issue":"6"},{"citation":{"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.","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","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.","short":"K.J. Painter, M. Winkler, SIAM Journal on Applied Mathematics 83 (2023) 2096–2117.","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.","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} }","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"},"publication":"SIAM Journal on Applied Mathematics","issue":"5","type":"journal_article","date_created":"2025-12-18T19:15:29Z","intvolume":" 83","date_updated":"2025-12-18T20:11:36Z","publication_status":"published","author":[{"last_name":"Painter","first_name":"Kevin J.","full_name":"Painter, Kevin J."},{"full_name":"Winkler, Michael","first_name":"Michael","last_name":"Winkler","id":"31496"}],"publication_identifier":{"issn":["0036-1399","1095-712X"]},"year":"2023","title":"Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities","status":"public","volume":83,"doi":"10.1137/22m1539393","user_id":"31496","_id":"63277","publisher":"Society for Industrial & Applied Mathematics (SIAM)","language":[{"iso":"eng"}],"page":"2096-2117"},{"citation":{"short":"M. Winkler, Zeitschrift Für Angewandte Mathematik Und Physik 74 (2023).","ama":"Winkler M. Global generalized solvability in a strongly degenerate taxis-type parabolic system modeling migration–consumption interaction. Zeitschrift für angewandte Mathematik und Physik. 2023;74(1). doi:10.1007/s00033-022-01925-3","chicago":"Winkler, Michael. “Global Generalized Solvability in a Strongly Degenerate Taxis-Type Parabolic System Modeling Migration–Consumption Interaction.” Zeitschrift Für Angewandte Mathematik Und Physik 74, no. 1 (2023). https://doi.org/10.1007/s00033-022-01925-3.","bibtex":"@article{Winkler_2023, title={Global generalized solvability in a strongly degenerate taxis-type parabolic system modeling migration–consumption interaction}, volume={74}, DOI={10.1007/s00033-022-01925-3}, number={132}, journal={Zeitschrift für angewandte Mathematik und Physik}, publisher={Springer Science and Business Media LLC}, author={Winkler, Michael}, year={2023} }","apa":"Winkler, M. (2023). Global generalized solvability in a strongly degenerate taxis-type parabolic system modeling migration–consumption interaction. Zeitschrift Für Angewandte Mathematik Und Physik, 74(1), Article 32. https://doi.org/10.1007/s00033-022-01925-3","mla":"Winkler, Michael. “Global Generalized Solvability in a Strongly Degenerate Taxis-Type Parabolic System Modeling Migration–Consumption Interaction.” Zeitschrift Für Angewandte Mathematik Und Physik, vol. 74, no. 1, 32, Springer Science and Business Media LLC, 2023, doi:10.1007/s00033-022-01925-3.","ieee":"M. Winkler, “Global generalized solvability in a strongly degenerate taxis-type parabolic system modeling migration–consumption interaction,” Zeitschrift für angewandte Mathematik und Physik, vol. 74, no. 1, Art. no. 32, 2023, doi: 10.1007/s00033-022-01925-3."},"status":"public","volume":74,"user_id":"31496","_id":"63283","publisher":"Springer Science and Business Media LLC","abstract":[{"text":"AbstractThe parabolic problem $$\\begin{aligned} \\left\\{ \\begin{array}{l} u_t=\\Delta \\big (u\\phi (v)\\big ), \\\\ v_t=\\Delta v-uv, \\end{array} \\right. \\end{aligned}$$\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n u\r\n t\r\n \r\n =\r\n Δ\r\n \r\n (\r\n \r\n u\r\n ϕ\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 \r\n \r\n \r\n \r\n \r\n \r\n v\r\n t\r\n \r\n =\r\n Δ\r\n v\r\n -\r\n u\r\n v\r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n is considered in smoothly bounded subdomains of $${\\mathbb {R}}^n$$\r\n \r\n \r\n R\r\n \r\n n\r\n \r\n with arbitrary $$n\\ge 1$$\r\n \r\n n\r\n ≥\r\n 1\r\n \r\n . Under the assumptions that $$\\phi \\in C^0([0,\\infty )) \\cap C^3((0,\\infty ))$$\r\n \r\n ϕ\r\n ∈\r\n \r\n C\r\n 0\r\n \r\n \r\n (\r\n \r\n [\r\n 0\r\n ,\r\n ∞\r\n )\r\n \r\n )\r\n \r\n ∩\r\n \r\n C\r\n 3\r\n \r\n \r\n (\r\n \r\n (\r\n 0\r\n ,\r\n ∞\r\n )\r\n \r\n )\r\n \r\n \r\n is positive on $$(0,\\infty )$$\r\n \r\n (\r\n 0\r\n ,\r\n ∞\r\n )\r\n \r\n and satisfies $$\\begin{aligned} \\liminf _{\\xi \\searrow 0} \\frac{\\phi (\\xi )}{\\xi ^\\alpha }>0 \\quad {\\text{ and }} \\quad \\limsup _{\\xi \\searrow 0} \\big \\{ \\xi ^\\beta |\\phi '(\\xi )| \\big \\}<\\infty \\end{aligned}$$\r\n \r\n \r\n \r\n \r\n \r\n \r\n lim inf\r\n \r\n ξ\r\n ↘\r\n 0\r\n \r\n \r\n \r\n \r\n ϕ\r\n (\r\n ξ\r\n )\r\n \r\n \r\n ξ\r\n α\r\n \r\n \r\n >\r\n 0\r\n \r\n \r\n \r\n and\r\n \r\n \r\n \r\n \r\n lim sup\r\n \r\n ξ\r\n ↘\r\n 0\r\n \r\n \r\n \r\n {\r\n \r\n \r\n ξ\r\n β\r\n \r\n \r\n |\r\n \r\n ϕ\r\n ′\r\n \r\n \r\n (\r\n ξ\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 some $$\\alpha >0$$\r\n \r\n α\r\n >\r\n 0\r\n \r\n and $$\\beta >0$$\r\n \r\n β\r\n >\r\n 0\r\n \r\n , for all reasonably regular initial data an associated no-flux type initial-boundary value problem is shown to admit a global solution in an appropriately generalized sense. This extends previously developed solution theories on problems of this form, which either concentrated on non-degenerate or weakly degenerate cases corresponding to the choices $$\\alpha =0$$\r\n \r\n α\r\n =\r\n 0\r\n \r\n and $$\\alpha \\in (0,2)$$\r\n \r\n α\r\n ∈\r\n (\r\n 0\r\n ,\r\n 2\r\n )\r\n \r\n , or were restricted to low-dimensional settings by requiring that $$n\\le 2$$\r\n \r\n n\r\n ≤\r\n 2\r\n \r\n .","lang":"eng"}],"issue":"1","publication":"Zeitschrift für angewandte Mathematik und Physik","type":"journal_article","date_created":"2025-12-18T19:17:51Z","intvolume":" 74","date_updated":"2025-12-18T20:12:20Z","publication_status":"published","author":[{"id":"31496","first_name":"Michael","last_name":"Winkler","full_name":"Winkler, Michael"}],"publication_identifier":{"issn":["0044-2275","1420-9039"]},"title":"Global generalized solvability in a strongly degenerate taxis-type parabolic system modeling migration–consumption interaction","year":"2023","doi":"10.1007/s00033-022-01925-3","language":[{"iso":"eng"}],"article_number":"32"},{"date_created":"2025-12-18T19:05:34Z","type":"journal_article","citation":{"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","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.","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} }","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","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."},"issue":"1","publication":"Applicable Analysis","_id":"63255","language":[{"iso":"eng"}],"publisher":"Informa UK Limited","page":"45-64","volume":103,"doi":"10.1080/00036811.2023.2173183","user_id":"31496","author":[{"full_name":"Li, Genglin","first_name":"Genglin","last_name":"Li"},{"id":"31496","first_name":"Michael","last_name":"Winkler","full_name":"Winkler, Michael"}],"publication_identifier":{"issn":["0003-6811","1563-504X"]},"title":"Refined regularity analysis for a Keller-Segel-consumption system involving signal-dependent motilities","status":"public","year":"2023","intvolume":" 103","date_updated":"2025-12-18T20:14:04Z","publication_status":"published"},{"date_updated":"2025-12-18T20:14:52Z","publication_status":"published","intvolume":" 41","title":"A quantitative strong parabolic maximum principle and application to a taxis-type migration–consumption model involving signal-dependent degenerate diffusion","year":"2023","author":[{"id":"31496","full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael"}],"publication_identifier":{"issn":["0294-1449","1873-1430"]},"doi":"10.4171/aihpc/73","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"\r\n The taxis-type migration–consumption model accounting for signal-dependent motilities, as given by \r\n \r\n u_{t} = \\Delta (u\\phi(v))\r\n \r\n , \r\n \r\n v_{t} = \\Delta v-uv\r\n \r\n , is considered for suitably smooth functions \r\n \r\n \\phi\\colon[0,\\infty)\\to\\R\r\n \r\n which are such that \r\n \r\n \\phi>0\r\n \r\n on \r\n \r\n (0,\\infty)\r\n \r\n , but that in addition \r\n \r\n \\phi(0)=0\r\n \r\n with \r\n \r\n \\phi'(0)>0\r\n \r\n . In order to appropriately cope with the diffusion degeneracies thereby included, this study separately examines the Neumann problem for the linear equation \r\n \r\n V_{t} = \\Delta V + \\nabla\\cdot ( a(x,t)V) + b(x,t)V\r\n \r\n and establishes a statement on how pointwise positive lower bounds for nonnegative solutions depend on the supremum and the mass of the initial data, and on integrability features of \r\n \r\n a\r\n \r\n and \r\n \r\n b\r\n \r\n . This is thereafter used as a key tool in the derivation of a result on global existence of solutions to the equation above, smooth and classical for positive times, under the mere assumption that the suitably regular initial data be nonnegative in both components. Apart from that, these solutions are seen to stabilize toward some equilibrium, and as a qualitative effect genuinely due to degeneracy in diffusion, a criterion on initial smallness of the second component is identified as sufficient for this limit state to be spatially nonconstant.\r\n "}],"issue":"1","publication":"Annales de l'Institut Henri Poincaré C, Analyse non linéaire","type":"journal_article","date_created":"2025-12-18T19:08:10Z","status":"public","user_id":"31496","volume":41,"page":"95-127","_id":"63261","publisher":"European Mathematical Society - EMS - Publishing House GmbH","citation":{"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, vol. 41, no. 1, European Mathematical Society - EMS - Publishing House GmbH, 2023, pp. 95–127, 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}, volume={41}, DOI={10.4171/aihpc/73}, number={1}, journal={Annales de l’Institut Henri Poincaré C, Analyse non linéaire}, publisher={European Mathematical Society - EMS - Publishing House GmbH}, author={Winkler, Michael}, year={2023}, pages={95–127} }","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. 2023;41(1):95-127. doi: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, vol. 41, no. 1, pp. 95–127, 2023, doi: 10.4171/aihpc/73.","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, 41(1), 95–127. https://doi.org/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 41, no. 1 (2023): 95–127. https://doi.org/10.4171/aihpc/73.","short":"M. Winkler, Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire 41 (2023) 95–127."}},{"publication":"Studies in Applied Mathematics","issue":"4","abstract":[{"lang":"eng","text":"AbstractWe give an overview of analytical results concerned with chemotaxis systems where the signal is absorbed. We recall results on existence and properties of solutions for the prototypical chemotaxis‐consumption model and various variants and review more recent findings on its ability to support the emergence of spatial structures."}],"date_created":"2024-04-07T12:50:45Z","type":"journal_article","keyword":["Applied Mathematics"],"author":[{"full_name":"Lankeit, Johannes","first_name":"Johannes","last_name":"Lankeit"},{"last_name":"Winkler","first_name":"Michael","full_name":"Winkler, Michael","id":"31496"}],"publication_identifier":{"issn":["0022-2526","1467-9590"]},"title":"Depleting the signal: Analysis of chemotaxis‐consumption models—A survey","year":"2023","intvolume":" 151","date_updated":"2025-12-18T20:16:04Z","publication_status":"published","language":[{"iso":"eng"}],"doi":"10.1111/sapm.12625","citation":{"mla":"Lankeit, Johannes, and Michael Winkler. “Depleting the Signal: Analysis of Chemotaxis‐consumption Models—A Survey.” Studies in Applied Mathematics, vol. 151, no. 4, Wiley, 2023, pp. 1197–229, doi:10.1111/sapm.12625.","bibtex":"@article{Lankeit_Winkler_2023, title={Depleting the signal: Analysis of chemotaxis‐consumption models—A survey}, volume={151}, DOI={10.1111/sapm.12625}, number={4}, journal={Studies in Applied Mathematics}, publisher={Wiley}, author={Lankeit, Johannes and Winkler, Michael}, year={2023}, pages={1197–1229} }","ama":"Lankeit J, Winkler M. Depleting the signal: Analysis of chemotaxis‐consumption models—A survey. Studies in Applied Mathematics. 2023;151(4):1197-1229. doi:10.1111/sapm.12625","ieee":"J. Lankeit and M. Winkler, “Depleting the signal: Analysis of chemotaxis‐consumption models—A survey,” Studies in Applied Mathematics, vol. 151, no. 4, pp. 1197–1229, 2023, doi: 10.1111/sapm.12625.","apa":"Lankeit, J., & Winkler, M. (2023). Depleting the signal: Analysis of chemotaxis‐consumption models—A survey. Studies in Applied Mathematics, 151(4), 1197–1229. https://doi.org/10.1111/sapm.12625","chicago":"Lankeit, Johannes, and Michael Winkler. “Depleting the Signal: Analysis of Chemotaxis‐consumption Models—A Survey.” Studies in Applied Mathematics 151, no. 4 (2023): 1197–1229. https://doi.org/10.1111/sapm.12625.","short":"J. Lankeit, M. Winkler, Studies in Applied Mathematics 151 (2023) 1197–1229."},"status":"public","_id":"53338","publisher":"Wiley","page":"1197-1229","volume":151,"user_id":"31496"}]