On asymptotic behaviors of solutions to parabolic systems modelling chemotaxis

Yoshiyuki Kagei; Yasunori Maekawa

doi:10.1016/j.jde.2012.08.028

On asymptotic behaviors of solutions to parabolic systems modelling chemotaxis

Yoshiyuki Kagei, Yasunori Maekawa

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

4 Citations (Scopus)

Abstract

This paper deals with large time behaviors of solutions to a Keller-Segel system which possesses self-similar solutions. By taking into account the invariant properties of the equation with respect to a scaling and translations, we show that suitably shifted self-similar solutions give more precise asymptotic profiles of general solutions at large time. The convergence rate is also computed in details.

Original language	English
Pages (from-to)	2951-2992
Number of pages	42
Journal	Journal of Differential Equations
Volume	253
Issue number	11
DOIs	https://doi.org/10.1016/j.jde.2012.08.028
Publication status	Published - Dec 1 2012

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.1016/j.jde.2012.08.028

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title = "On asymptotic behaviors of solutions to parabolic systems modelling chemotaxis",

abstract = "This paper deals with large time behaviors of solutions to a Keller-Segel system which possesses self-similar solutions. By taking into account the invariant properties of the equation with respect to a scaling and translations, we show that suitably shifted self-similar solutions give more precise asymptotic profiles of general solutions at large time. The convergence rate is also computed in details.",

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AB - This paper deals with large time behaviors of solutions to a Keller-Segel system which possesses self-similar solutions. By taking into account the invariant properties of the equation with respect to a scaling and translations, we show that suitably shifted self-similar solutions give more precise asymptotic profiles of general solutions at large time. The convergence rate is also computed in details.

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On asymptotic behaviors of solutions to parabolic systems modelling chemotaxis

Abstract

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