Strong time periodic solutions to Keller-Segel systems: an approach by the quasilinear Arendt-Bu theorem

DOI10.1016/j.jde.2020.01.020zbMath1437.35671OpenAlexW3002981959WikidataQ126320901 ScholiaQ126320901MaRDI QIDQ1989452

Christian Stinner, Matthias Hieber

Publication date: 22 April 2020

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2020.01.020

zbMATH Keywords

quasilinear evolution equationsstrong periodic solutionsKeller-Segel systems

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Periodic solutions to PDEs (35B10) PDEs in connection with biology, chemistry and other natural sciences (35Q92) General theory of partial differential operators (47F05) Cell movement (chemotaxis, etc.) (92C17) Strong solutions to PDEs (35D35) Quasilinear parabolic equations (35K59)

Related Items (5)

Strong time-periodic solutions to chemotaxis-Navier-Stokes equations on bounded domains ⋮ Strong periodic solutions to quasilinear parabolic equations: An approach by the Da Prato–Grisvard theorem ⋮ Time periodic solutions to Hibler’s sea ice model ⋮ The Keller-Segel system on bounded convex domains in critical spaces ⋮ If time were a graph, what would evolution equations look like?

Cites Work

• Unnamed Item
• Unnamed Item
• Pattern formation of the attraction-repulsion Keller-Segel system
• Finite-time blowup and global-in-time unbounded solutions to a parabolic-parabolic quasilinear Keller-Segel system in higher dimensions
• Boundedness in a quasilinear parabolic-parabolic Keller-Segel system with subcritical sensitivity
• The operator-valued Marcinkiewicz multiplier theorem and maximal regularity
• A user's guide to PDE models for chemotaxis
• Global strong solution to the semi-linear Keller-Segel system of parabolic-parabolic type with small data in scale invariant spaces
• From 1970 until present: The Keller-Segel model in chemotaxis and its consequences. I
• New thoughts on old results of R. T. Seeley
• Periodic traveling waves in a reaction-diffusion model with chemotaxis and nonlocal delay effect
• Global existence of solutions to an \(n\)-dimensional parabolic-parabolic system for chemotaxis with logistic-type growth and superlinear production
• On a time-dependent bio-reactor model with chemotaxis.
• New critical exponents in a fully parabolic quasilinear Keller-Segel system and applications to volume filling models
• Time-periodic and stable patterns of a two-competing-species Keller-Segel chemotaxis model: effect of cellular growth
• Moving Interfaces and Quasilinear Parabolic Evolution Equations
• <i>L</i>_<i>p</i>-Estimates of Solutions to <i>n</i>-Dimensional Parabolic-Parabolic System for Chemotaxis with Subquadratic Degradation
• MULTISCALE BIOLOGICAL TISSUE MODELS AND FLUX-LIMITED CHEMOTAXIS FOR MULTICELLULAR GROWING SYSTEMS
• ℛ-boundedness, Fourier multipliers and problems of elliptic and parabolic type
• Analysis in Banach Spaces
• Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues

This page was built for publication: Strong time periodic solutions to Keller-Segel systems: an approach by the quasilinear Arendt-Bu theorem