Global existence and asymptotic behavior in a two-species chemotaxis system with logistic source
type: Item
instance of: scholarly article
title: Global existence and asymptotic behavior in a two-species chemotaxis system with logistic source
zbMATH Open document ID: 1442.35037
author: Guoqiang Ren
author: Bin Liu
published in: Journal of Differential Equations
publication date: 2020-04-22T00:00:00Z
review text: The authors study two-species chemotaxis system with Lotka-Volterra competitive kinetics \begin{align*} u_t&=d_1\Delta u-\nabla\cdot (u\chi_1(w)\nabla w)+\mu_1u(1-u-a_1v) \\ v_t&=d_2\Delta v-\nabla\cdot (v\chi_2(w)\nabla w)+\mu_2v(1-v-a_2u) \\ w_t&=d_3\Delta w-(\alpha u+\beta v)w \quad \text{in }\Omega\times (0,\infty) \end{align*} with \[ \left. \frac{\partial}{\partial n}(u,v,w)\right\vert_{\partial\Omega}=0, \quad 0\leq \left. (u,v,w)\right\vert_{t=0}=(u_0, v_0, w_0) \in W^{1,\infty}(\Omega)^3, \] where \(\Omega\subset\mathbb{R}^N\) is a bounded domain with smooth boundary \(\partial\Omega\) and \(d_j\) for \(j=1,2,3\), \(\mu_i\), \(a_i\) for \(i=1,2\), \(\alpha\), \(\beta\) are positive constants, and \(0<\chi_i\in C^{1,\theta}([0, \infty))\), \(i=1,2\), Then there is \(A=A(d_1, d_3)>0\) explicitly given such that if \[ \Vert w_0\Vert_\infty <\overline{w}\equiv \frac{A(d_1, d_3)}{\Vert \chi_1\Vert_{L^\infty[0,\Vert w_0\Vert_\infty]}}, \] there is a weak solution global-in-time which belogs to \begin{align*} u&\in L^\infty(0,\infty; L^1(\Omega))\cap L^2_{\mathrm{loc}}([0, \infty; W^{1,2}(\Omega)) \\ v&\in L^\infty(0,\infty; L^1(\Omega)) \\ w&\in L^\infty(\Omega\times (0,\infty))\cap L^2_{\mathrm{loc}}([0,\infty); W^{1,2}(\Omega)), \end{align*} where this weak solution is defined in the standard weak form with respect to \(u\) and \(w\), while a combination of an inequality derived from the multiplication of \(\frac{\psi}{v+1}\) for the test function \(\psi\) to the super-solution to the second equation and the other inequality valid for the sub-solution to it, \[ \int_\Omega v\leq \mu_1\int_\Omega v(1-v-a_2u). \] The proof relies on the approximate solution classical global-in-time for the truncated nonlinearity, and then the compactness argument for the passage to the limit.
reviewed by: Takashi Suzuki
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35D30
Mathematics Subject Classification ID: 35A01
Mathematics Subject Classification ID: 92C17
Mathematics Subject Classification ID: 35K51
zbMATH DE Number: 7191484
zbMATH Keywords: chemotaxis
zbMATH Keywords: Lotka-Volterra competitive kinetics
zbMATH Keywords: global existence
zbMATH Keywords: asymptotic stability
MaRDI profile type: Publication
full work available at URL: j.jde.2020.01.008
OpenAlex ID: W3001217687
cites work: Equilibration in a fully parabolic two-species chemotaxis system with competitive kinetics
cites work: Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues
cites work: Global existence and asymptotic stability in a competitive two-species chemotaxis system with two signals
cites work: Global Very Weak Solutions to a Chemotaxis-Fluid System with Nonlinear Diffusion
cites work: Q4398321
cites work: A user's guide to PDE models for chemotaxis
cites work: Boundedness and stabilization in a two-dimensional two-species chemotaxis-Navier-Stokes system with competitive kinetics
cites work: From 1970 until present: The Keller-Segel model in chemotaxis and its consequences. I
cites work: Boundedness vs. blow-up in a chemotaxis system
cites work: Boundedness in quasilinear Keller-Segel systems of parabolic-parabolic type on non-convex bounded domains
cites work: Boundedness and stabilization in a two-species chemotaxis-competition system with signal-dependent diffusion and sensitivity
cites work: An optimal result for global existence in a three-dimensional Keller-Segel-Navier-Stokes system involving tensor-valued sensitivity with saturation
cites work: Initiation of slime mold aggregation viewed as an instability
cites work: Traveling bands of chemotactic bacteria: a theoretical analysis
cites work: Q5562267
cites work: Locally bounded global solutions to a chemotaxis consumption model with singular sensitivity and nonlinear diffusion
cites work: On the global generalized solvability of a chemotaxis model with signal absorption and logistic growth terms
cites work: A generalized solution concept for the Keller-Segel system with logarithmic sensitivity: global solvability for large nonradial data
cites work: On a fully parabolic chemotaxis system with Lotka-Volterra competitive kinetics
cites work: Convergence of global and bounded solutions of a two-species chemotaxis model with a logistic source
cites work: Boundedness in a two-species chemotaxis system
cites work: A new approach toward stabilization in a two-species chemotaxis model with logistic source
cites work: GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR IN A THREE-DIMENSIONAL TWO-SPECIES CHEMOTAXIS-STOKES SYSTEM WITH TENSOR-VALUED SENSITIVITY
cites work: Boundedness and decay property in a three-dimensional Keller-Segel-Stokes system involving tensor-valued sensitivity with saturation
cites work: Boundedness and asymptotic stability in a two-species chemotaxis-competition model with signal-dependent sensitivity
cites work: Global existence and asymptotic stability of solutions to a two-species chemotaxis system with any chemical diffusion
cites work: Q4381941
cites work: Asymptotic stability of a two species chemotaxis system with non-diffusive chemoattractant
cites work: On a Two Species Chemotaxis Model with Slow Chemical Diffusion
cites work: Global boundedness and asymptotic behavior in a two-species chemotaxis-competition system with two signals
cites work: Global boundedness of solutions to a chemotaxis-fluid system with singular sensitivity and logistic source
cites work: Global existence of bounded solutions for a quasilinear chemotaxis system with logistic source
cites work: Global weak solutions in a chemotaxis system with large singular sensitivity
cites work: Boundedness in a quasilinear parabolic-parabolic Keller-Segel system with subcritical sensitivity
cites work: Eventual smoothness and stabilization of large-data solutions in a three-dimensional chemotaxis system with consumption of chemoattractant
cites work: Global boundedness versus finite-time blow-up of solutions to a quasilinear fully parabolic Keller-Segel system of two species
cites work: Boundedness and asymptotic stability of solutions to a two-species chemotaxis system with consumption of chemoattractant
cites work: Global weak solutions in a three-dimensional Keller–Segel–Navier–Stokes system with subcritical sensitivity
cites work: Asymptotic dynamics on a singular chemotaxis system modeling onset of tumor angiogenesis
cites work: Absence of collapse in a parabolic chemotaxis system with signal-dependent sensitivity
cites work: Aggregation vs. global diffusive behavior in the higher-dimensional Keller-Segel model
cites work: Global Large-Data Solutions in a Chemotaxis-(Navier–)Stokes System Modeling Cellular Swimming in Fluid Drops
cites work: Stabilization in a two-dimensional chemotaxis-Navier-Stokes system
cites work: Large-Data Global Generalized Solutions in a Chemotaxis System with Tensor-Valued Sensitivities
cites work: The two-dimensional Keller-Segel system with singular sensitivity and signal absorption: global large-data solutions and their relaxation properties
cites work: How far do chemotaxis-driven forces influence regularity in the Navier-Stokes system?
cites work: Renormalized radial large-data solutions to the higher-dimensional Keller-Segel system with singular sensitivity and signal absorption
cites work: A three-dimensional Keller-Segel-Navier-Stokes system with logistic source: global weak solutions and asymptotic stabilization
cites work: Global generalized solutions to a multi-dimensional doubly tactic resource consumption model accounting for social interactions
cites work: Stabilization in the logarithmic Keller-Segel system
cites work: Criteria on global boundedness versus finite time blow-up to a two-species chemotaxis system with two chemicals
cites work: Competitive exclusion for a two-species chemotaxis system with two chemicals
cites work: Global boundedness of solutions to a two-species chemotaxis system
cites work: Global solutions in a high-dimensional two-species chemotaxis model with Lotka-Volterra competitive kinetics
cites work: Global existence and asymptotic behavior of solutions to a two-species chemotaxis system with two chemicals
cites work: Boundedness and stabilization in a two-species chemotaxis system with signal absorption
cites work: Boundedness in a two-species quasi-linear chemotaxis system with two chemicals

Global existence and asymptotic behavior in a two-species chemotaxis system with logistic source (cites work)
cites work: An optimal result for global existence and boundedness in a three-dimensional Keller-Segel-Stokes system with nonlinear diffusion

Global existence and asymptotic behavior in a two-species chemotaxis system with logistic source (Wikidata QID)
Wikidata QID: Q126313610

Global existence and asymptotic behavior in a two-species chemotaxis system with logistic source (DOI)
DOI: 10.1016/J.JDE.2020.01.008

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