Global existence of solutions to an \(n\)-dimensional parabolic-parabolic system for chemotaxis with logistic-type growth and superlinear production

zbMath1391.35189MaRDI QIDQ1704393

Koichi Osaki, Etsushi Nakaguchi

Publication date: 9 March 2018

Published in: Osaka Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.ojm/1515661216

zbMATH Keywords

chemotaxisglobal existenceparabolic systemlogistic-type growthsuperlinear production

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) PDEs in connection with biology, chemistry and other natural sciences (35Q92) A priori estimates in context of PDEs (35B45) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Cell movement (chemotaxis, etc.) (92C17) Initial-boundary value problems for second-order parabolic systems (35K51)

Related Items (14)

Global existence and stability in a two-species chemotaxis system ⋮ Global boundedness of solutions resulting from both the self-diffusion and the logistic-type source ⋮ Strong periodic solutions to quasilinear parabolic equations: An approach by the Da Prato–Grisvard theorem ⋮ Boundedness and Asymptotic Stability in a Chemotaxis Model with Signal-Dependent Motility and Nonlinear Signal Secretion ⋮ Boundedness in a fully parabolic chemotaxis system with logistic-type source and nonlinear production ⋮ Strong time periodic solutions to Keller-Segel systems: an approach by the quasilinear Arendt-Bu theorem ⋮ A semilinear heat equation with initial data in negative Sobolev spaces ⋮ Relaxed parameter conditions for chemotactic collapse in logistic-type parabolic-elliptic Keller-Segel systems ⋮ Boundedness for a fully parabolic Keller-Segel model with sublinear segregation and superlinear aggregation ⋮ Boundedness in a nonlinear attraction-repulsion Keller-Segel system with production and consumption ⋮ On a fully parabolic chemotaxis system with source term and periodic asymptotic behavior ⋮ The Keller-Segel system on bounded convex domains in critical spaces ⋮ Immediate smoothing and global solutions for initial data inL¹×W^1,2in a Keller–Segel system with logistic terms in 2D ⋮ Large-data solutions in a three-dimensional chemotaxis-haptotaxis system with remodeling of non-diffusible attractant: the role of sub-linear production of diffusible signal

Cites Work

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• Global solutions and exponential attractors of a parabolic-parabolic system for chemotaxis with subquadratic degradation
• Global existence and boundedness of classical solutions for a chemotaxis model with logistic source
• Nondegeneracy of blow-up points for the parabolic Keller-Segel system
• Global existence of solutions to a parabolic-parabolic system for chemotaxis with weak degradation
• 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
• Initiation of slime mold aggregation viewed as an instability
• Chemotaxis with logistic source: very weak global solutions and their boundedness properties
• Aggregation vs. global diffusive behavior in the higher-dimensional Keller-Segel model
• A user's guide to PDE models for chemotaxis
• From 1970 until present: The Keller-Segel model in chemotaxis and its consequences. I
• Mathematical biology. Vol. 2: Spatial models and biomedical applications.
• From 1970 until present: the Keller-Segel model in chemotaxis and its consequences. II
• Partial differential equations. 2: Qualitative studies of linear equations
• Global existence and boundedness of classical solutions to a parabolic-parabolic chemotaxis system
• Eventual smoothness and asymptotics in a three-dimensional chemotaxis system with logistic source
• Overview of mathematical approaches used to model bacterial chemotaxis. II: Bacterial popu\-lations
• Boundedness and global existence in the higher-dimensional parabolic -- parabolic chemotaxis system with/without growth source
• Boundedness in quasilinear Keller-Segel systems of parabolic-parabolic type on non-convex bounded domains
• Boundedness vs. blow-up in a chemotaxis system
• Blow-up in a chemotaxis model without symmetry assumptions
• <i>L</i>_<i>p</i>-Estimates of Solutions to <i>n</i>-Dimensional Parabolic-Parabolic System for Chemotaxis with Subquadratic Degradation
• Abstract Parabolic Evolution Equations and their Applications
• Boundedness in the Higher-Dimensional Parabolic-Parabolic Chemotaxis System with Logistic Source

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