On a quasilinear parabolic-elliptic chemotaxis system with logistic source

DOI10.1016/j.jde.2013.12.007zbMath1301.35060OpenAlexW2019738448MaRDI QIDQ2437984

Liangchen Wang, Pan Zheng, Chun-Lai Mu

Publication date: 10 March 2014

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

Full work available at URL: https://doi.org/10.1016/j.jde.2013.12.007

zbMATH Keywords

boundednesschemotaxisglobal existencelogistic source

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Cell movement (chemotaxis, etc.) (92C17) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Initial-boundary value problems for mixed-type systems of PDEs (35M33)

Related Items (only showing first 100 items - show all)

Critical mass capacity for two-dimensional Keller–Segel model with nonlocal reaction terms ⋮ Finite-time blow-up of solution for a chemotaxis model with singular sensitivity and logistic source ⋮ An attraction‐repulsion chemotaxis system with logistic source ⋮ Boundedness of classical solutions to a chemotaxis consumption system with signal dependent motility and logistic source ⋮ On some properties of a linearized quasi-hydrodynamical system of equations ⋮ The effects of cross-diffusion and logistic source on the boundedness of solutions to a pursuit-evasion model ⋮ Boundedness and large time behavior for flux limitation in a two-species chemotaxis system ⋮ Finite-time blow-up in the Cauchy problem of a Keller-Segel system with logistic source ⋮ Global dynamics in a chemotaxis system involving nonlinear indirect signal secretion and logistic source ⋮ Combined effects of nonlinear diffusion and gradient-dependent flux limitation on a chemotaxis-haptotaxis model ⋮ Dynamic behavior analysis to a generalized chemotaxis-consumption system ⋮ Dynamics in a parabolic-elliptic chemotaxis system with logistic source involving exponents depending on the spatial variables ⋮ Global boundedness for a chemotaxis system involving nonlinear indirect consumption mechanism ⋮ Blow-up analysis to a quasilinear chemotaxis system with nonlocal logistic effect ⋮ Dynamics in a parabolic-elliptic chemotaxis system with growth source and nonlinear secretion ⋮ A quasilinear attraction-repulsion chemotaxis system of parabolic-elliptic type with logistic source ⋮ Pattern formation for a nonlinear diffusion chemotaxis model with logistic source ⋮ Boundedness in a three-dimensional chemotaxis-fluid system involving tensor-valued sensitivity with saturation ⋮ On a macrophage and tumor cell chemotaxis system with both paracrine and autocrine loops ⋮ Global boundedness in a quasilinear attraction-repulsion chemotaxis model with nonlinear sensitivity ⋮ Persistence and convergence in parabolic-parabolic chemotaxis system with logistic source on \(\mathbb{R}^N\) ⋮ Eventual smoothness and stabilization in a three-dimensional Keller-Segel-Navier-Stokes system modeling coral fertilization ⋮ Boundedness and blow up in the higher-dimensional attraction-repulsion chemotaxis system with nonlinear diffusion ⋮ On a parabolic-elliptic system with chemotaxis and logistic type growth ⋮ Finite-time blow-up in low-dimensional Keller-Segel systems with logistic-type superlinear degradation ⋮ A new result for global solvability and boundedness in the \(N\)-dimensional quasilinear chemotaxis model with logistic source and consumption of chemoattractant ⋮ Global existence of solutions and uniform persistence of a diffusive predator-prey model with prey-taxis ⋮ Global existence, regularity and boundedness in a higher-dimensional chemotaxis-Navier-Stokes system with nonlinear diffusion and general sensitivity ⋮ Boundedness in a quasilinear 2D parabolic-parabolic attraction-repulsion chemotaxis system ⋮ Global boundedness and decay for a multi-dimensional chemotaxis-haptotaxis system with nonlinear diffusion ⋮ Chemotaxis model with nonlocal nonlinear reaction in the whole space ⋮ Global boundedness of solutions to a quasilinear parabolic-parabolic Keller-Segel system with variable logistic source ⋮ Improvement of conditions for boundedness in a fully parabolic chemotaxis system with nonlinear signal production ⋮ Spreading speeds and traveling waves of a parabolic-elliptic chemotaxis system with logistic source on \(\mathbb{R}^N\) ⋮ Boundedness and global asymptotic stability of constant equilibria in a fully parabolic chemotaxis system with nonlinear logistic source ⋮ Infinite time blow-up of many solutions to a general quasilinear parabolic-elliptic Keller-Segel system ⋮ Existence of traveling wave solutions to parabolic-elliptic-elliptic chemotaxis systems with logistic source ⋮ On a parabolic-elliptic chemotaxis-growth system with nonlinear diffusion ⋮ A quasilinear parabolic-parabolic chemotaxis model with logistic source and singular sensitivity ⋮ Global boundedness and large time behavior of solutions to a chemotaxis system with flux limitation ⋮ Global existence and boundedness of classical solutions in a quasilinear parabolic-elliptic chemotaxis system with logistic source ⋮ Boundedness and asymptotic behavior in a fully parabolic chemotaxis-growth system with signal-dependent sensitivity ⋮ Boundedness in a three-component chemotaxis system with nonlinear diffusion for Alopecia areata ⋮ Finite-time blow-up in a quasilinear chemotaxis system with an external signal consumption ⋮ Blow-up of nonradial solutions to the hyperbolic-elliptic chemotaxis system with logistic source ⋮ Large time behavior of solutions to a fully parabolic chemotaxis-haptotaxis model in \(N\) dimensions ⋮ Global boundedness of solutions to a quasilinear chemotaxis system with nonlocal nonlinear reaction ⋮ A new (and optimal) result for the boundedness of a solution of a quasilinear chemotaxis-haptotaxis model (with a logistic source) ⋮ Mathematical Research for Models Which is Related to Chemotaxis System ⋮ Persistence property in a two-species chemotaxis system with two signals ⋮ Global large-data generalized solutions in a chemotactic movement with rotational flux caused by two stimuli ⋮ Global existence and boundedness in a quasilinear attraction-repulsion chemotaxis system of parabolic-elliptic type ⋮ Global weak solutions of a parabolic-elliptic Keller-Segel system with gradient dependent chemotactic coefficients ⋮ Blow-up prevention by logistic source in an \(N\)-D chemotaxis-convection model of capillary-sprout growth during tumor angiogenesis ⋮ Global solutions of a two-dimensional chemotaxis system with attraction and repulsion rotational flux terms ⋮ A new result for the global existence (and boundedness) and regularity of a three-dimensional Keller-Segel-Navier-Stokes system modeling coral fertilization ⋮ Global existence to an attraction-repulsion chemotaxis model with fast diffusion and nonlinear source ⋮ Boundedness of solutions in a chemotaxis system with nonlinear sensitivity and logistic source ⋮ Boundedness in the higher-dimensional quasilinear chemotaxis-growth system with indirect attractant production ⋮ Boundedness and blow-up for a chemotaxis system with generalized volume-filling effect and logistic source ⋮ Boundedness of solutions to a quasilinear parabolic-parabolic Keller-Segel system with a logistic source ⋮ Global existence to a higher-dimensional quasilinear chemotaxis system with consumption of chemoattractant ⋮ Large time behavior of solutions to a quasilinear attraction-repulsion chemotaxis system with logistic source ⋮ A blow-up result for a quasilinear chemotaxis system with logistic source in higher dimensions ⋮ Parabolic-elliptic chemotaxis model with space-time dependent logistic sources on \(\mathbb{R}^N\). II: Existence, uniqueness, and stability of strictly positive entire solutions ⋮ Boundedness in a three-dimensional chemotaxis-haptotaxis model with nonlinear diffusion ⋮ Global existence and asymptotic behavior of classical solutions to a parabolic-elliptic chemotaxis system with logistic source on \(\mathbb{R}^N\) ⋮ Global existence of solutions to an attraction-repulsion chemotaxis model with growth ⋮ Global boundedness in a two-competing-species chemotaxis system with two chemicals ⋮ A new result for global existence and boundedness of solutions to a parabolic-parabolic Keller-Segel system with logistic source ⋮ A new result for boundedness of solutions to a higher-dimensional quasilinear chemotaxis system with a logistic source ⋮ Boundedness in a three-dimensional Keller-Segel-Stokes system involving tensor-valued sensitivity with saturation ⋮ Global existence and asymptotic behavior of the fractional chemotaxis system with signal-dependent sensitivity ⋮ Boundedness of solutions to a quasilinear chemotaxis-haptotaxis model ⋮ Boundedness in quasilinear Keller-Segel equations with nonlinear sensitivity and logistic source ⋮ A parabolic-elliptic-elliptic attraction-repulsion chemotaxis system with logistic source ⋮ Lower bounds for the blow-up time in a superlinear hyperbolic equation with linear damping term ⋮ Boundedness and stabilization of solutions to a chemotaxis May-Nowak model ⋮ A new result for boundedness and stabilization in a two-species chemotaxis system with two chemicals ⋮ Global existence and asymptotic behavior of classical solutions to a fractional logistic Keller-Segel system ⋮ Numerical study of vanishing and spreading dynamics of chemotaxis systems with logistic source and a free boundary ⋮ Logistic type attraction-repulsion chemotaxis systems with a free boundary or unbounded boundary, I. Asymptotic dynamics in fixed unbounded domain ⋮ On a fully parabolic chemotaxis system with nonlinear signal secretion ⋮ A blow-up result for the chemotaxis system with nonlinear signal production and logistic source ⋮ Nonlocal nonlinear reaction preventing blow-up in supercritical case of chemotaxis system ⋮ Improvement of conditions for boundedness in a two-species chemotaxis competition system of parabolic-parabolic-elliptic type ⋮ Global classical solutions in a chemotaxis(-Navier)-Stokes system with indirect signal production ⋮ A quasilinear parabolic–elliptic chemotaxis-growth system with nonlinear secretion ⋮ A new result on existence of global bounded classical solution to a attraction-repulsion chemotaxis system with logistic source ⋮ Finite-time blow-up in a higher-dimensional quasilinear parabolic-elliptic chemotaxis system with space dependent logistic source ⋮ Large time behavior of solution to quasilinear chemotaxis system with logistic source ⋮ Boundedness of solutions to a quasilinear parabolic-elliptic Keller-Segel system with logistic source ⋮ Finite-time blow-up and global boundedness for chemotaxis system with strong logistic dampening ⋮ Global existence and boundedness of classical solutions for a chemotaxis model with consumption of chemoattractant and logistic source ⋮ Global classical solutions, stability of constant equilibria, and spreading speeds in attraction-repulsion chemotaxis systems with logistic source on \(\mathbb{R}^{N}\) ⋮ Convergence rate of a quasilinear parabolic-elliptic chemotaxis system with logistic source ⋮ A blow-up result for attraction-repulsion system with nonlinear signal production and generalized logistic source ⋮ Boundedness of solutions in a quasilinear chemo-repulsion system with nonlinear signal production ⋮ Blow-up prevention by quadratic degradation in a higher-dimensional chemotaxis-growth model with indirect attractant production ⋮ Dynamics in a Quasilinear Parabolic-Elliptic Keller-Segel System with Generalized Logistic Source and Nonlinear Secretion

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Boundedness in a parabolic-parabolic quasilinear chemotaxis system with logistic source
• Global existence and boundedness of classical solutions for a chemotaxis model with logistic source
• Finite-time blowup and global-in-time unbounded solutions to a parabolic-parabolic quasilinear Keller-Segel system in higher dimensions
• Global existence vs. blowup in a fully parabolic quasilinear 1D 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
• Finite time blow-up for a one-dimensional quasilinear parabolic-parabolic chemotaxis system
• Quasilinear nonuniformly parabolic system modelling chemotaxis
• Chemotaxis with logistic source: very weak global solutions and their boundedness properties
• Model of chemotaxis with threshold density and singular diffusion
• Aggregation vs. global diffusive behavior in the higher-dimensional Keller-Segel model
• A user's guide to PDE models for chemotaxis
• Boundedness and finite-time collapse in a chemotaxis system with volume-filling effect
• Infinite-dimensional dynamical systems in mechanics and physics.
• Elliptic partial differential equations of second order
• Global existence and boundedness of classical solutions to a parabolic-parabolic chemotaxis system
• Competitive exclusion in a two-species chemotaxis model
• Finite-time blow-up in the higher-dimensional parabolic-parabolic Keller-Segel system
• On the global existence of solutions to an aggregation model
• Finite-time blowup in a supercritical quasilinear parabolic-parabolic Keller-Segel system in dimension 2
• Boundedness vs. blow-up in a chemotaxis system
• Blow-up in a chemotaxis model without symmetry assumptions
• Absence of collapse in a parabolic chemotaxis system with signal-dependent sensitivity
• Singularity formation in chemotaxis systems with volume-filling effect
• A Chemotaxis-Haptotaxis Model: The Roles of Nonlinear Diffusion and Logistic Source
• Finite-time blow-up in a quasilinear system of chemotaxis
• On Chemotaxis Models with Cell Population Interactions
• Classical solutions and pattern formation for a volume filling chemotaxis model
• Does a ‘volume-filling effect’ always prevent chemotactic collapse?
• L^PBounds of solutions of reaction-diffusion equations
• On Explosions of Solutions to a System of Partial Differential Equations Modelling Chemotaxis
• Global Regularity versus Infinite-Time Singularity Formation in a Chemotaxis Model with Volume-Filling Effect and Degenerate Diffusion
• COMPETING EFFECTS OF ATTRACTION VS. REPULSION IN CHEMOTAXIS
• Boundedness in the Higher-Dimensional Parabolic-Parabolic Chemotaxis System with Logistic Source
• A Chemotaxis System with Logistic Source
• Global existence for a parabolic chemotaxis model with prevention of overcrowding

This page was built for publication: On a quasilinear parabolic-elliptic chemotaxis system with logistic source