Stabilization in the logarithmic Keller-Segel system

DOI10.1016/j.na.2018.01.002zbMath1391.35066OpenAlexW2793165141MaRDI QIDQ2412983

Tomomi Yokota, Michael Winkler

Publication date: 6 April 2018

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2018.01.002

zbMATH Keywords

large time behaviorexponential ratehomogeneous Neumann boundary conditionssingular sensitivity

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Degenerate parabolic equations (35K65) Cell movement (chemotaxis, etc.) (92C17) Initial-boundary value problems for second-order parabolic systems (35K51)

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Cites Work

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• Global boundedness of solutions in a parabolic-parabolic chemotaxis system with singular sensitivity
• Multiple radial positive solutions of semilinear elliptic problems with Neumann boundary conditions
• Bubbling on boundary submanifolds for the Lin-Ni-Takagi problem at higher critical exponents
• Boundedness in a fully parabolic chemotaxis system with singular sensitivity
• Global existence and asymptotic behavior of classical solutions to a parabolic-elliptic chemotaxis system with logistic source on \(\mathbb{R}^N\)
• Global weak solutions in a chemotaxis system with large singular sensitivity
• Initiation of slime mold aggregation viewed as an instability
• Traveling bands of chemotactic bacteria: a theoretical analysis
• On convergence to equilibria for the Keller-Segel chemotaxis model
• Global existence and boundedness in a parabolic-elliptic Keller-Segel system with general sensitivity
• Aggregation vs. global diffusive behavior in the higher-dimensional Keller-Segel model
• Large amplitude stationary solutions to a chemotaxis system
• Geometric theory of semilinear parabolic equations
• Steady-state distribution of bacteria chemotactic toward oxygen
• Finite-time blow-up in the higher-dimensional parabolic-parabolic Keller-Segel system
• Boundedness and global asymptotic stability of constant equilibria in a fully parabolic chemotaxis system with nonlinear logistic source
• A generalized solution concept for the Keller-Segel system with logarithmic sensitivity: global solvability for large nonradial data
• An optimal bound on the number of interior spike solutions for the Lin-Ni-Takagi problem
• Global asymptotic stability of constant equilibria in a fully parabolic chemotaxis system with strong logistic dampening
• Boundedness vs. blow-up in a chemotaxis system
• Blow-up in a chemotaxis model without symmetry assumptions
• A new approach toward boundedness in a two-dimensional parabolic chemotaxis system with singular sensitivity
• Global existence and boundedness of radial solutions to a two dimensional fully parabolic chemotaxis system with general sensitivity
• Global solutions in a fully parabolic chemotaxis system with singular sensitivity
• A unified method for boundedness in fully parabolic chemotaxis systems with signal‐dependent sensitivity
• Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues
• A Chemotaxis System with Logistic Source
• The Lin-Ni’s problem for mean convex domains