Global boundedness of solutions to a chemotaxis–haptotaxis model with tissue remodeling
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Publication:4630535
DOI10.1142/S0218202518400134zbMath1416.35052OpenAlexW2806489871MaRDI QIDQ4630535
Publication date: 27 March 2019
Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1142/s0218202518400134
PDEs in connection with biology, chemistry and other natural sciences (35Q92) A priori estimates in context of PDEs (35B45) Cell movement (chemotaxis, etc.) (92C17) Quasilinear parabolic equations (35K59) Initial-boundary value problems for second-order parabolic systems (35K51)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Boundedness in a three-dimensional chemotaxis-haptotaxis model
- Boundedness properties of very weak solutions to a fully parabolic chemotaxis-system with logistic source
- 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
- Global existence for a degenerate haptotaxis model of cancer invasion
- Global existence of a two-dimensional chemotaxis-haptotaxis model with remodeling of non-diffusible attractant
- Global existence for a haptotaxis model of cancer invasion with tissue remodeling
- 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
- Mathematical modelling of cancer invasion of tissue: dynamic heterogeneity
- Boundedness and decay enforced by quadratic degradation in a three-dimensional chemotaxis-fluid system
- Chemotaxis with logistic source: very weak global solutions and their boundedness properties
- Local existence and uniqueness of regular solutions in a model of tissue invasion by solid tumours
- Global existence of classical solutions to a combined chemotaxis-haptotaxis model with logistic source
- An application of the invariance principle to reaction diffusion equations
- Eventual smoothness and asymptotics in a three-dimensional chemotaxis system with logistic source
- Boundedness in a quasilinear fully parabolic Keller-Segel system of higher dimension with logistic source
- Boundedness in quasilinear Keller-Segel systems of parabolic-parabolic type on non-convex bounded domains
- Energy-type estimates and global solvability in a two-dimensional chemotaxis-haptotaxis model with remodeling of non-diffusible attractant
- Boundedness vs. blow-up in a chemotaxis system
- Boundedness in a chemotaxis–haptotaxis model with nonlinear diffusion
- Global existence for a go-or-grow multiscale model for tumor invasion with therapy
- Global Weak Solutions in a PDE-ODE System Modeling Multiscale Cancer Cell Invasion
- Boundedness and stabilization in a multi-dimensional chemotaxis—haptotaxis model
- ASYMPTOTIC BEHAVIOR OF GLOBAL SOLUTIONS TO A MODEL OF CELL INVASION
- Large Time Behavior in a Multidimensional Chemotaxis-Haptotaxis Model with Slow Signal Diffusion
- A multiscale model for pH-tactic invasion with time-varying carrying capacities
- 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
- On Explosions of Solutions to a System of Partial Differential Equations Modelling Chemotaxis
- Global classical solution and boundedness to a chemotaxis-haptotaxis model with re-establishment mechanisms
- ANALYSIS OF A MATHEMATICAL MODEL OF TUMOR LYMPHANGIOGENESIS
- CONVERGENCE OF A CANCER INVASION MODEL TO A LOGISTIC CHEMOTAXIS MODEL
- Boundedness in the Higher-Dimensional Parabolic-Parabolic Chemotaxis System with Logistic Source
- Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues
- On a structured multiscale model for acid-mediated tumor invasion: The effects of adhesion and proliferation
- GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR OF A TUMOR ANGIOGENESIS MODEL WITH CHEMOTAXIS AND HAPTOTAXIS
- 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
- Large time behavior of solution to a fully parabolic chemotaxis-haptotaxis model in higher dimensions
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