Global existence and asymptotic properties of the solution to a two-species chemotaxis system

DOI10.1016/j.jmaa.2014.03.084zbMath1395.35039OpenAlexW1980337697MaRDI QIDQ489041

Qingshan Zhang, Yuxiang Li

Publication date: 27 January 2015

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2014.03.084

zbMATH Keywords

self-similar solutionglobal existenceasymptotic profiletwo-species chemotaxis system

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Initial value problems for second-order parabolic systems (35K45) Cell movement (chemotaxis, etc.) (92C17) Self-similar solutions to PDEs (35C06)

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Cites Work

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• Generalizing the Keller-Segel model: Lyapunov functionals, steady state analysis, and blow-up results for multi-species chemotaxis models in the presence of attraction and repulsion between competitive interacting species
• Existence and uniqueness theorem on mild solutions to the Keller-Segel system in the scaling invariant space
• On asymptotic behaviors of solutions to parabolic systems modelling chemotaxis
• Initiation of slime mold aggregation viewed as an instability
• Global solutions and self-similar solutions of semilinear parabolic equations with nonlinear gradient terms
• Aggregation vs. global diffusive behavior in the higher-dimensional Keller-Segel model
• A user's guide to PDE models for chemotaxis
• Large time behavior of the vorticity two-dimensional viscous flow and its application to vortex formation
• Asymptotically self-similar global solutions of the nonlinear Schrödinger and heat equations
• Large time behavior for convection-diffusion equations in \(\mathbb{R}{} ^ N\)
• From 1970 until present: The Keller-Segel model in chemotaxis and its consequences. I
• From 1970 until present: the Keller-Segel model in chemotaxis and its consequences. II
• Global existence and blowup of solutions to a chemotaxis system.
• Blowup in higher dimensional two species chemotactic systems
• Asymptotic decay for the solutions of the parabolic-parabolic Keller-Segel chemotaxis system in critical spaces
• ASYMPTOTIC SELF-SIMILAR BEHAVIOR OF SOLUTIONS FOR A SEMILINEAR PARABOLIC SYSTEM
• Stabilization in a two-species chemotaxis system with a logistic source
• Remarks on the blowup and global existence for a two species chemotactic Keller–Segel system in²
• The Keller-Segel system of parabolic-parabolic type with initial data in weak $L^{n/2}(\mathbb{R}^n)$ and its application to self-similar solutions
• Simultaneous finite time blow-up in a two-species model for chemotaxis
• Decay Properties and Asymptotic Profiles of Bounded Solutions to a Parabolic System of Chemotaxis in Rn
• Self-similarity in chemotaxis systems
• Asymptotically self-similar global solutions of a general semilinear heat equation
• Global existence, asymptotic behavior and self-similar solutions for a class of semilinear parabolic systems