Global existence and uniform boundedness in a chemotaxis model with signal-dependent motility

DOI10.1016/j.jde.2021.07.029zbMath1472.35401arXiv2101.10666OpenAlexW3187221303MaRDI QIDQ2045860

Jie Jiang, Philippe Laurençot

Publication date: 16 August 2021

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

Full work available at URL: https://arxiv.org/abs/2101.10666

zbMATH Keywords

comparison principlechemotaxisparabolic-elliptic systemsignal-dependent motility

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Degenerate parabolic equations (35K65) Comparison principles in context of PDEs (35B51)

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Cites Work

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• Dual semigroups and second order linear elliptic boundary value problems
• Dynamic theory of quasilinear parabolic equations. II: Reaction-diffusion systems
• Comparison methods for a Keller-Segel-type model of pattern formations with density-suppressed motilities
• Initiation of slime mold aggregation viewed as an instability
• Model for chemotaxis
• Dynamic theory of quasilinear parabolic systems. III: Global existence
• An application of the invariance principle to reaction diffusion equations
• Subsolutions for elliptic equations in \(L^1\)
• Solutions to a Penrose-Fife model of phase-field type
• Composition in fractional Sobolev spaces.
• Global existence of weak solutions to a signal-dependent Keller-Segel model for local sensing chemotaxis
• Global existence for a kinetic model of pattern formation with density-suppressed motilities
• A logarithmic chemotaxis model featuring global existence and aggregation
• Singularities of solutions to chemotaxis systems
• Singularity patterns in a chemotaxis model
• Dynamic theory of quasilinear parabolic equations—I. Abstract evolution equations
• On Explosions of Solutions to a System of Partial Differential Equations Modelling Chemotaxis
• Global well-posedness and stability of constant equilibria in parabolic–elliptic chemotaxis systems without gradient sensing
• A sufficient condition of sensitivity functions for boundedness of solutions to a parabolic-parabolic chemotaxis system
• Effects of signal-dependent motilities in a Keller–Segel-type reaction–diffusion system
• Delayed blow‐up for chemotaxis models with local sensing
• Critical mass on the Keller-Segel system with signal-dependent motility
• Boundedness of solutions to parabolic-elliptic Keller-Segel systems with signal-dependent sensitivity