Blow-up profiles and refined extensibility criteria in quasilinear Keller-Segel systems

DOI10.1016/j.jmaa.2018.03.052OpenAlexW2794732050MaRDI QIDQ1747080

Marcel Freitag

Publication date: 3 May 2018

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.2018.03.052

zbMATH Keywords

blow-upcritical exponentsnonlinear parabolic equationsclassical solutionscell movement (chemotaxis etc.)

Mathematics Subject Classification ID

Ordinary differential equations (34-XX) Partial differential equations (35-XX)

Related Items

Exponential grow-up rates in a quasilinear Keller–Segel system ⋮ Arbitrarily fast grow-up rates in quasilinear Keller–Segel systems ⋮ Global existence of solutions to the chemotaxis system with logistic source under nonlinear Neumann boundary conditions ⋮ Global boundedness in a 3D quasilinear Keller-Segel-Stokes system with nonlinear sensitivity and indirect signal production ⋮ Properties of given and detected unbounded solutions to a class of chemotaxis models ⋮ Global existence of solutions in some chemotaxis systems with sub-logistic source under nonlinear Neumann boundary conditions in 2d ⋮ Global weak solutions of a parabolic-elliptic Keller-Segel system with gradient dependent chemotactic coefficients ⋮ The fast signal diffusion limit in nonlinear chemotaxis systems ⋮ Facing low regularity in chemotaxis systems ⋮ Fluid interaction does not affect the critical exponent in a three-dimensional Keller-Segel-Stokes model ⋮ A refined criterion and lower bounds for the blow-up time in a parabolic-elliptic chemotaxis system with nonlinear diffusion ⋮ Explicit lower bound of blow-up time for an attraction-repulsion chemotaxis system ⋮ Effect of nonlinear diffusion on a lower bound for the blow-up time in a fully parabolic chemotaxis system ⋮ On the optimality of upper estimates near blow-up in quasilinear Keller–Segel systems ⋮ Blow-up profiles in quasilinear fully parabolic Keller–Segel systems

Cites Work

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• Finite-time blowup and global-in-time unbounded solutions to a parabolic-parabolic quasilinear Keller-Segel system in higher dimensions
• Global bounded solutions of the higher-dimensional Keller-Segel system under smallness conditions in optimal spaces
• Boundedness in a quasilinear parabolic-parabolic Keller-Segel system with subcritical sensitivity
• Initiation of slime mold aggregation viewed as an instability
• Quasilinear nonuniformly parabolic system modelling chemotaxis
• A user's guide to PDE models for chemotaxis
• The effects of nutrient chemotaxis on bacterial aggregation patterns with non-linear degenerate cross diffusion
• New critical exponents in a fully parabolic quasilinear Keller-Segel system and applications to volume filling models
• Finite-time blow-up in the higher-dimensional parabolic-parabolic Keller-Segel system
• Corrigendum to: ``Nondegeneracy of blow-up points for the parabolic Keller-Segel system
• On the global existence of solutions to an aggregation model
• Boundedness vs. blow-up in a chemotaxis system
• Partial differential equations of chemotaxis and angiogenesis
• Blow-up in a chemotaxis model without symmetry assumptions
• Global existence for a go-or-grow multiscale model for tumor invasion with therapy
• Bacterial swimming and oxygen transport near contact lines
• Global Weak Solutions in a PDE-ODE System Modeling Multiscale Cancer Cell Invasion
• Does a ‘volume-filling effect’ always prevent chemotactic collapse?
• Global Behaviour of a Reaction-Diffusion System Modelling Chemotaxis
• Volume Filling Effect in Modelling Chemotaxis
• Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues

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