Finite-time blow-up for quasilinear degenerate Keller-Segel systems of parabolic-parabolic type

DOI10.1016/j.jde.2018.01.038zbMath1394.35253OpenAlexW2793539358MaRDI QIDQ1704551

Sachiko Ishida, Takahiro Hashira, Tomomi Yokota

Publication date: 12 March 2018

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2018.01.038

zbMATH Keywords

chemotaxisfinite-time blow-upquasilinear degenerate Keller-Segel systems

Mathematics Subject Classification ID

PDEs in connection with biology, chemistry and other natural sciences (35Q92) Degenerate parabolic equations (35K65) Cell movement (chemotaxis, etc.) (92C17) Blow-up in context of PDEs (35B44)

Related Items (21)

Weak stabilization in degenerate parabolic equations in divergence form: application to degenerate Keller-Segel systems ⋮ Global existence and boundedness in a supercritical quasilinear degenerate Keller-Segel system under relaxed smallness conditions for initial data ⋮ Repulsion effects on boundedness in the higher dimensional fully parabolic attraction-repulsion chemotaxis system ⋮ On effects of the nonlinear signal production to the boundedness and finite-time blow-up in a flux-limited chemotaxis model ⋮ Finite-time blow-up in a quasilinear degenerate chemotaxis system with flux limitation ⋮ How strongly does diffusion or logistic-type degradation affect existence of global weak solutions in a chemotaxis-Navier-Stokes system? ⋮ Positivity-preserving high-order compact difference method for the Keller-Segel chemotaxis model ⋮ Critical mass phenomena in higher dimensional quasilinear Keller–Segel systems with indirect signal production ⋮ Finite-time blow-up for quasilinear degenerate Keller-Segel systems of parabolic-parabolic type ⋮ Existence of weak solutions for porous medium equation with a divergence type of drift term ⋮ Global weak solutions to a 3-dimensional degenerate and singular chemotaxis-Navier-Stokes system with logistic source ⋮ Boundedness and finite-time blow-up in a chemotaxis system with nonlinear signal production ⋮ Keller-Segel chemotaxis models: a review ⋮ Extensibility criterion ruling out gradient blow-up in a quasilinear degenerate chemotaxis system with flux limitation ⋮ Properties of blow-up solutions and their initial data for quasilinear degenerate Keller-Segel systems of parabolic-parabolic type ⋮ Boundedness in a nonlinear attraction-repulsion Keller-Segel system with production and consumption ⋮ Facing low regularity in chemotaxis systems ⋮ Blow-up analysis of solutions for weakly coupled degenerate parabolic systems with nonlinear boundary conditions ⋮ Effect of nonlinear diffusion on a lower bound for the blow-up time in a fully parabolic chemotaxis system ⋮ Finite-time blow-up in quasilinear parabolic-elliptic chemotaxis system with nonlinear signal production ⋮ Finite-time blow-up in a quasilinear degenerate parabolic-elliptic chemotaxis system with logistic source and nonlinear production

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