Boundedness in a quasilinear fully parabolic Keller-Segel system via maximal Sobolev regularity
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Publication:2178727
DOI10.3934/dcdss.2020012zbMath1439.35225OpenAlexW2914611093WikidataQ128457311 ScholiaQ128457311MaRDI QIDQ2178727
Publication date: 11 May 2020
Published in: Discrete and Continuous Dynamical Systems. Series S (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.3934/dcdss.2020012
Stability in context of PDEs (35B35) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Initial-boundary value problems for second-order parabolic systems (35K51)
Related Items (12)
Weak stabilization in degenerate parabolic equations in divergence form: application to degenerate Keller-Segel systems ⋮ Global weak solutions in a three-dimensional Keller-Segel-Navier-Stokes system with indirect signal production ⋮ Blow-up phenomena for a chemotaxis system with flux limitation ⋮ On effects of the nonlinear signal production to the boundedness and finite-time blow-up in a flux-limited chemotaxis model ⋮ Behavior in time of solutions of a Keller-Segel system with flux limitation and source term ⋮ Boundedness and weak stabilization in a degenerate chemotaxis model arising from tumor invasion ⋮ Boundedness through nonlocal dampening effects in a fully parabolic chemotaxis model with sub and superquadratic growth ⋮ Hölder estimates of weak solutions to degenerate chemotaxis systems with a source term ⋮ Extensibility criterion ruling out gradient blow-up in a quasilinear degenerate chemotaxis system with flux limitation ⋮ Boundedness in a nonlinear attraction-repulsion Keller-Segel system with production and consumption ⋮ Weak solutions to a class of signal-dependent motility Keller-Segel systems with superlinear damping ⋮ Effect of nonlinear diffusion on a lower bound for the blow-up time in a fully parabolic chemotaxis system
Cites Work
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- An iterative approach to \(L^\infty\)-boundedness in quasilinear Keller-Segel systems
- Hölder regularity and uniqueness theorem on weak solutions to the degenerate Keller-Segel system
- Boundedness in a three-dimensional chemotaxis-haptotaxis model
- Gradient estimate for solutions to quasilinear non-degenerate Keller-Segel systems on \(\mathbb{R}^N\)
- Blow-up in finite or infinite time for quasilinear degenerate Keller-Segel systems of parabolic-parabolic type
- Finite-time blowup and global-in-time unbounded solutions to a parabolic-parabolic quasilinear Keller-Segel system in higher dimensions
- Remarks on the global existence of weak solutions to quasilinear degenerate Keller-Segel systems
- Boundedness in a quasilinear parabolic-parabolic Keller-Segel system with subcritical sensitivity
- Global existence of weak solutions to quasilinear degenerate Keller-Segel systems of parabolic-parabolic type
- Global existence of weak solutions to quasilinear degenerate Keller-Segel systems of parabolic-parabolic type with small data
- On uniqueness theorem on weak solutions to the parabolic-parabolic Keller-Segel system of degenerate and singular types
- Initiation of slime mold aggregation viewed as an instability
- A user's guide to PDE models for chemotaxis
- Compact sets in the space \(L^ p(0,T;B)\)
- Finite-time blow-up in the higher-dimensional parabolic-parabolic Keller-Segel system
- Boundedness in quasilinear Keller-Segel systems of parabolic-parabolic type on non-convex bounded domains
- A quasi-linear parabolic system of chemotaxis
- Global existence and decay properties for a degenerate Keller-Segel model with a power factor in drift term
- Does a ‘volume-filling effect’ always prevent chemotactic collapse?
- Heat kernels and maximal lp—lqestimates for parabolic evolution equations
- Maximal regularity for parabolic equations with inhomogeneous boundary conditions in Sobolev spaces with mixed $L_p$-norm
- Possibility of the existence of blow‐up solutions to quasilinear degenerate Keller–Segel systems of parabolic–parabolic type
- Large Time Behavior in a Chemotaxis Model with Nonlinear General Diffusion for Tumor Invasion
- Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues
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