Local and global existence of solutions to a quasilinear degenerate chemotaxis system with unbounded initial data

DOI10.1002/MMA.3780zbMath1354.35175OpenAlexW2149807798MaRDI QIDQ3188501

Noriaki Yoshino, Tomomi Yokota

Publication date: 11 August 2016

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mma.3780

zbMATH Keywords

weak solutionschemotaxisquasilinear degenerate diffusion

Mathematics Subject Classification ID

Nonlinear accretive operators, dissipative operators, etc. (47H06) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Weak solutions to PDEs (35D30) Cell movement (chemotaxis, etc.) (92C17) Initial-boundary value problems for second-order parabolic systems (35K51)

Related Items (2)

Global existence of solutions and uniform persistence of a diffusive predator-prey model with prey-taxis ⋮ A parabolic-elliptic chemotaxis system with nonlinear diffusion approached from a Cahn-Hilliard-type system

Cites Work

• Unnamed Item
• Unnamed Item
• Blow-up in finite or infinite time for quasilinear degenerate Keller-Segel systems of parabolic-parabolic type
• 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
• Global existence of weak solutions to quasilinear degenerate Keller-Segel systems of parabolic-parabolic type
• Initiation of slime mold aggregation viewed as an instability
• A user's guide to PDE models for chemotaxis
• Functional analysis, Sobolev spaces and partial differential equations
• Well-posedness for chemotaxis dynamics with nonlinear cell diffusion
• Existence of solutions to chemotaxis dynamics with Lipschitz diffusion and superlinear growth
• Finite-time blow-up in the higher-dimensional parabolic-parabolic Keller-Segel system
• Boundedness in quasilinear Keller-Segel systems of parabolic-parabolic type on non-convex bounded domains
• The Hele-Shaw asymptotics for mechanical models of tumor growth
• Global existence and decay properties for a degenerate Keller-Segel model with a power factor in drift term
• Singularity formation in chemotaxis systems with volume-filling effect
• Does a ‘volume-filling effect’ always prevent chemotactic collapse?
• Lyapunov functions and L^p-estimates for a class of reaction-diffusion systems
• An Asymptotic Solution to a Nonlinear Reaction-Diffusion System with Chemotaxis
• Possibility of the existence of blow‐up solutions to quasilinear degenerate Keller–Segel systems of parabolic–parabolic type

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