Boundedness in the higher-dimensional chemotaxis-haptotaxis model with nonlinear diffusion
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Publication:890222
DOI10.1016/j.jde.2015.09.051zbMath1332.35152OpenAlexW1922175155MaRDI QIDQ890222
Publication date: 9 November 2015
Published in: Journal of Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jde.2015.09.051
Smoothness and regularity of solutions to PDEs (35B65) Nonlinear parabolic equations (35K55) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Cell movement (chemotaxis, etc.) (92C17) Initial-boundary value problems for second-order parabolic systems (35K51)
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Cites Work
- Unnamed Item
- Unnamed Item
- Boundedness in a parabolic-parabolic quasilinear chemotaxis system with logistic source
- Finite-time blowup and global-in-time unbounded solutions to a parabolic-parabolic quasilinear Keller-Segel system in higher dimensions
- Nondegeneracy of blow-up points for the parabolic Keller-Segel system
- Boundedness in a quasilinear parabolic-parabolic Keller-Segel system with subcritical sensitivity
- Exponential attractor for a chemotaxis-growth system of equations
- Blow-up in a higher-dimensional chemotaxis system despite logistic growth restriction
- Initiation of slime mold aggregation viewed as an instability
- Quasilinear nonuniformly parabolic system modelling chemotaxis
- Mathematical modelling of cancer invasion of tissue: dynamic heterogeneity
- Chemotaxis with logistic source: very weak global solutions and their boundedness properties
- Global existence of classical solutions to a combined chemotaxis-haptotaxis model with logistic source
- Boundedness and finite-time collapse in a chemotaxis system with volume-filling effect
- Boundedness in quasilinear Keller-Segel systems of parabolic-parabolic type on non-convex bounded domains
- Boundedness vs. blow-up in a chemotaxis system
- Boundedness and stabilization in a multi-dimensional chemotaxis—haptotaxis model
- ASYMPTOTIC BEHAVIOR OF GLOBAL SOLUTIONS TO A MODEL OF CELL INVASION
- A Chemotaxis-Haptotaxis Model: The Roles of Nonlinear Diffusion and Logistic Source
- Finite-time blow-up in a quasilinear system of chemotaxis
- Global solution for a chemotactic–haptotactic model of cancer invasion
- BOUNDEDNESS OF SOLUTIONS OF A HAPTOTAXIS MODEL
- A Combined Chemotaxis-haptotaxis System: The Role of Logistic Source
- Global Existence of Classical Solutions for a Haptotaxis Model
- MATHEMATICAL MODELLING OF CANCER INVASION OF TISSUE: THE ROLE AND EFFECT OF NONLOCAL INTERACTIONS
- LPBounds of solutions of reaction-diffusion equations
- Boundedness in the Higher-Dimensional Parabolic-Parabolic Chemotaxis System with Logistic Source
- Dominance of chemotaxis in a chemotaxis–haptotaxis model
- MATHEMATICAL MODELLING OF CANCER CELL INVASION OF TISSUE: THE ROLE OF THE UROKINASE PLASMINOGEN ACTIVATION SYSTEM
- Blowup of nonradial solutions to parabolic-elliptic systems modeling chemotaxis in two-dimensional domains
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