Global convergence of a kinetic model of chemotaxis to a perturbed Keller-Segel model

Fabio A.C.C. Chalub; Kyungkeun Kang

doi:10.1016/j.na.2005.04.048

Global convergence of a kinetic model of chemotaxis to a perturbed Keller-Segel model

Fabio A.C.C. Chalub, Kyungkeun Kang

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

We consider a class of kinetic models of chemotaxis with two positive non-dimensional parameters coupled to a parabolic equation of the chemo-attractant. If both parameters are set equal zero, we have the classical Keller-Segel model for chemotaxis. We prove global existence of solutions of this two-parameters kinetic model and prove convergence of this model to models of chemotaxis with global existence when one of these two parameters is set equal zero. In one case, we find as a limit model a kinetic model of chemotaxis while in the other case we find a perturbed Keller-Segel model with global existence of solutions.

Original language	English
Pages (from-to)	686-695
Number of pages	10
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	64
Issue number	4
DOIs	https://doi.org/10.1016/j.na.2005.04.048
Publication status	Published - 2006 Feb 15

Bibliographical note

Funding Information:
FACCC was supported by FCT/Portugal through the Project FCT-POCTI/34471/MAT/2000. Both authors thank the kind hospitality of the Max Planck Institute for Mathematics in the Sciences (Leipzig, Germany), particularly to Angela Stevens, who suggested this problem.

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.1016/j.na.2005.04.048

Cite this

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title = "Global convergence of a kinetic model of chemotaxis to a perturbed Keller-Segel model",

abstract = "We consider a class of kinetic models of chemotaxis with two positive non-dimensional parameters coupled to a parabolic equation of the chemo-attractant. If both parameters are set equal zero, we have the classical Keller-Segel model for chemotaxis. We prove global existence of solutions of this two-parameters kinetic model and prove convergence of this model to models of chemotaxis with global existence when one of these two parameters is set equal zero. In one case, we find as a limit model a kinetic model of chemotaxis while in the other case we find a perturbed Keller-Segel model with global existence of solutions.",

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AU - Kang, Kyungkeun

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N2 - We consider a class of kinetic models of chemotaxis with two positive non-dimensional parameters coupled to a parabolic equation of the chemo-attractant. If both parameters are set equal zero, we have the classical Keller-Segel model for chemotaxis. We prove global existence of solutions of this two-parameters kinetic model and prove convergence of this model to models of chemotaxis with global existence when one of these two parameters is set equal zero. In one case, we find as a limit model a kinetic model of chemotaxis while in the other case we find a perturbed Keller-Segel model with global existence of solutions.

AB - We consider a class of kinetic models of chemotaxis with two positive non-dimensional parameters coupled to a parabolic equation of the chemo-attractant. If both parameters are set equal zero, we have the classical Keller-Segel model for chemotaxis. We prove global existence of solutions of this two-parameters kinetic model and prove convergence of this model to models of chemotaxis with global existence when one of these two parameters is set equal zero. In one case, we find as a limit model a kinetic model of chemotaxis while in the other case we find a perturbed Keller-Segel model with global existence of solutions.

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Global convergence of a kinetic model of chemotaxis to a perturbed Keller-Segel model

Abstract

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