Global existence and boundedness in a chemorepulsion system with superlinear diffusion

DOI10.3934/dcds.2018258zbMath1400.35160OpenAlexW2888371726WikidataQ129321153 ScholiaQ129321153MaRDI QIDQ1791660

Marcel Freitag

Publication date: 10 October 2018

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2018258

zbMATH Keywords

blow-upcritical exponentsnonlinear parabolic equationsclassical solutionscell movement (chemotaxisetc.

Mathematics Subject Classification ID

Initial-boundary value problems for higher-order parabolic equations (35K35) Critical exponents in context of PDEs (35B33) Cell movement (chemotaxis, etc.) (92C17) Blow-up in context of PDEs (35B44) Initial-boundary value problems for second-order parabolic systems (35K51) Classical solutions to PDEs (35A09)

Related Items (10)

Study of a chemo-repulsion model with quadratic production. II: Analysis of an unconditionally energy-stable fully discrete scheme ⋮ On a two-species attraction-repulsion chemotaxis system with nonlocal terms ⋮ Existence of weak solutions for porous medium equation with a divergence type of drift term ⋮ Keller-Segel chemotaxis models: a review ⋮ Some remarks on well-posedness of the higher-dimensional chemorepulsion system ⋮ Boundedness in a two-dimensional Keller-Segel-Navier-Stokes system involving a rapidly diffusing repulsive signal ⋮ A chemorepulsion model with superlinear production: analysis of the continuous problem and two approximately positive and energy-stable schemes ⋮ Strong damping effect of chemo-repulsion prevents blow-up ⋮ On a quasilinear fully parabolic attraction or repulsion chemotaxis system with nonlinear signal production ⋮ Asymptotic behaviors and existence of traveling wave solutions to the Keller-Segel model with logarithmic sensitivity

Cites Work

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• Global dynamics in a higher-dimensional repulsion chemotaxis model with nonlinear sensitivity
• 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
• Global bounded solutions of the higher-dimensional Keller-Segel system under smallness conditions in optimal spaces
• Locally bounded global solutions to a chemotaxis consumption model with singular sensitivity and nonlinear diffusion
• 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
• Aggregation vs. global diffusive behavior in the higher-dimensional Keller-Segel model
• A user's guide to PDE models for chemotaxis
• Compact sets in the space \(L^ p(0,T;B)\)
• Gagliardo-Nirenberg, composition and products in fractional Sobolev spaces
• 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
• On the global existence of solutions to an aggregation model
• Boundedness vs. blow-up in a chemotaxis system
• A quasi-linear parabolic system of chemotaxis
• Stabilization in a chemotaxis model for tumor invasion
• 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
• Absence of collapse in a parabolic chemotaxis system with signal-dependent sensitivity
• 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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