Boundedness of solutions in a chemotaxis system with nonlinear sensitivity and logistic source
From MaRDI portal
Publication:481985
DOI10.1016/j.jmaa.2014.11.031zbMath1307.35069OpenAlexW2085293341MaRDI QIDQ481985
Pan Zheng, Ya Tian, Xue-Gang Hu, Chun-Lai Mu
Publication date: 19 December 2014
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.2014.11.031
A priori estimates in context of PDEs (35B45) Cell movement (chemotaxis, etc.) (92C17) Semilinear parabolic equations (35K58)
Related Items
Boundedness of solutions in a fully parabolic quasilinear chemotaxis model with two species and two chemicals ⋮ Pattern formation for a nonlinear diffusion chemotaxis model with logistic source ⋮ Persistence and convergence in parabolic-parabolic chemotaxis system with logistic source on \(\mathbb{R}^N\) ⋮ On a generalized volume-filling chemotaxis system with nonlinear signal production ⋮ Global boundedness and decay for a multi-dimensional chemotaxis-haptotaxis system with nonlinear diffusion ⋮ Spreading speeds and traveling waves of a parabolic-elliptic chemotaxis system with logistic source on \(\mathbb{R}^N\) ⋮ Mathematical modeling and its analysis for instability of the immune system induced by chemotaxis ⋮ Existence of traveling wave solutions to parabolic-elliptic-elliptic chemotaxis systems with logistic source ⋮ Global existence and decay for a chemotaxis-growth system with generalized volume-filling effect and sublinear secretion ⋮ Boundedness of solutions to a quasilinear parabolic-parabolic chemotaxis model with nonlinear signal production ⋮ Boundedness and asymptotic behavior in a fully parabolic chemotaxis-growth system with signal-dependent sensitivity ⋮ Finite-time blow-up in a quasilinear chemotaxis system with an external signal consumption ⋮ On a quasilinear fully parabolic predator-prey model with indirect pursuit-evasion interaction ⋮ Persistence property in a two-species chemotaxis system with two signals ⋮ Global weak solutions of a parabolic-elliptic Keller-Segel system with gradient dependent chemotactic coefficients ⋮ Global existence of bounded solutions for a quasilinear chemotaxis system with logistic source ⋮ Global existence and asymptotic behavior of classical solutions to a parabolic-elliptic chemotaxis system with logistic source on \(\mathbb{R}^N\) ⋮ Global existence of solutions to an attraction-repulsion chemotaxis model with growth ⋮ Global boundedness in a two-competing-species chemotaxis system with two chemicals ⋮ Global existence and asymptotic behavior of the fractional chemotaxis system with signal-dependent sensitivity ⋮ Boundedness in the higher dimensional attraction-repulsion chemotaxis-growth system ⋮ Keller-Segel chemotaxis models: a review ⋮ Global existence and asymptotic behavior of classical solutions to a fractional logistic Keller-Segel system ⋮ Numerical study of vanishing and spreading dynamics of chemotaxis systems with logistic source and a free boundary ⋮ Logistic type attraction-repulsion chemotaxis systems with a free boundary or unbounded boundary, I. Asymptotic dynamics in fixed unbounded domain ⋮ Global classical solutions, stability of constant equilibria, and spreading speeds in attraction-repulsion chemotaxis systems with logistic source on \(\mathbb{R}^{N}\) ⋮ Convergence rate of a quasilinear parabolic-elliptic chemotaxis system with logistic source ⋮ Boundedness of solutions in a quasilinear chemo-repulsion system with nonlinear signal production ⋮ Global boundedness in a quasilinear chemotaxis system with signal-dependent sensitivity ⋮ Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues ⋮ Boundedness in a quasilinear chemotaxis-haptotaxis model of parabolic-parabolic-ODE type
Cites Work
- Unnamed Item
- Unnamed Item
- Chemotaxis can prevent thresholds on population density
- Boundedness in a parabolic-parabolic quasilinear chemotaxis system with logistic source
- Global solutions and exponential attractors of a parabolic-parabolic system for chemotaxis with subquadratic degradation
- Global existence and boundedness of classical solutions for a chemotaxis model with logistic source
- 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
- How far can chemotactic cross-diffusion enforce exceeding carrying capacities?
- Boundedness in a chemotaxis model with oxygen consumption by bacteria
- Time global existence and asymptotic behavior of solutions to generate quasi-linear parabolic systems of chemotaxis.
- Global existence of solutions to a parabolic-parabolic system for chemotaxis with weak degradation
- Exponential attractor for a chemotaxis-growth system of equations
- Initiation of slime mold aggregation viewed as an instability
- Chemotaxis with logistic source: very weak global solutions and their boundedness properties
- Aggregation vs. global diffusive behavior in the higher-dimensional Keller-Segel model
- A user's guide to PDE models for chemotaxis
- Boundedness and finite-time collapse in a chemotaxis system with volume-filling effect
- Geometric theory of semilinear parabolic equations
- Infinite-dimensional dynamical systems in mechanics and physics.
- 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 boundedness of classical solutions to a parabolic-parabolic chemotaxis system
- Boundedness in a quasilinear parabolic-parabolic Keller-Segel system with logistic source
- On a quasilinear parabolic-elliptic chemotaxis system with logistic source
- Global asymptotic stability of constant equilibria in a fully parabolic chemotaxis system with strong logistic dampening
- Boundedness vs. blow-up in a chemotaxis system
- Global existence and decay properties for a degenerate Keller-Segel model with a power factor in drift term
- Random walk with persistence and external bias
- Absence of collapse in a parabolic chemotaxis system with signal-dependent sensitivity
- Finite-time blow-up in a quasilinear system of chemotaxis
- Abstract Parabolic Evolution Equations and their Applications
- LPBounds of solutions of reaction-diffusion equations
- On Explosions of Solutions to a System of Partial Differential Equations Modelling Chemotaxis
- COMPETING EFFECTS OF ATTRACTION VS. REPULSION IN CHEMOTAXIS
- Boundedness in the Higher-Dimensional Parabolic-Parabolic Chemotaxis System with Logistic Source
- A Chemotaxis System with Logistic Source
- Boundedness of solutions to a quasilinear parabolic-elliptic Keller-Segel system with logistic source