A new criterion to a two-chemical substances chemotaxis system with critical dimension

DOI10.3934/dcdsb.2018074zbMath1409.35038OpenAlexW2781661767MaRDI QIDQ1756846

Suying Liu, Xue-Li Bai

Publication date: 27 December 2018

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdsb.2018074

zbMATH Keywords

small initial datahomogeneous Neumann conditionsglobal boundedness of solutions

Mathematics Subject Classification ID

PDEs in connection with biology, chemistry and other natural sciences (35Q92) A priori estimates in context of PDEs (35B45) Cell movement (chemotaxis, etc.) (92C17) Blow-up in context of PDEs (35B44) Quasilinear parabolic equations (35K59) Initial-boundary value problems for second-order parabolic systems (35K51)

Related Items (6)

Global boundedness of a chemotaxis model with logistic growth and general indirect signal production ⋮ Boundedness in a chemotaxis-fluid system involving a saturated sensitivity and indirect signal production mechanism ⋮ Global generalized solutions to a chemotaxis model of capillary-sprout growth during tumor angiogenesis ⋮ Unnamed Item ⋮ Large time behavior in a chemotaxis model with logistic growth and indirect signal production ⋮ Emergence of lager densities in chemotaxis system with indirect signal production and non-radial symmetry case

Cites Work

• Application of an Adams type inequality to a two-chemical substances chemotaxis system
• A user's guide to PDE models for chemotaxis
• From 1970 until present: The Keller-Segel model in chemotaxis and its consequences. I
• L^PBounds of solutions of reaction-diffusion equations
• Heat kernels and maximal l^p—l^qestimates for parabolic evolution equations
• Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues

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