Instability induced by cross-diffusion in reaction-diffusion systems

Canrong Tian; Zhigui Lin; Michael Pedersen

doi:10.1016/j.nonrwa.2009.01.043

Instability induced by cross-diffusion in reaction-diffusion systems

Canrong Tian, Zhigui Lin, Michael Pedersen

Yangzhou University

Research output: Contribution to journal › Journal article › Research › peer-review

Abstract

In this paper the instability of the uniform equilibrium of a general strongly coupled reaction–diffusion is discussed. In unbounded domain and bounded domain the sufficient
conditions for the instability are obtained respectively. The conclusion is applied to the ecosystem, it is shown that cross-diffusion can induce the instability of an equilibrium
which is stable for the kinetic system and for the self-diffusion–reaction system.

Original language	English
Journal	Nonlinear Analysis: Real World Applications
Volume	11
Issue number	2
Pages (from-to)	1036-1045
ISSN	1468-1218
DOIs	https://doi.org/10.1016/j.nonrwa.2009.01.043
Publication status	Published - 2010

Keywords

Instability
Cross-diffusion
Pattern formation

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abstract = "In this paper the instability of the uniform equilibrium of a general strongly coupled reaction–diffusion is discussed. In unbounded domain and bounded domain the sufficientconditions for the instability are obtained respectively. The conclusion is applied to the ecosystem, it is shown that cross-diffusion can induce the instability of an equilibriumwhich is stable for the kinetic system and for the self-diffusion–reaction system.",

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T1 - Instability induced by cross-diffusion in reaction-diffusion systems

AU - Tian, Canrong

AU - Lin, Zhigui

AU - Pedersen, Michael

PY - 2010

Y1 - 2010

N2 - In this paper the instability of the uniform equilibrium of a general strongly coupled reaction–diffusion is discussed. In unbounded domain and bounded domain the sufficientconditions for the instability are obtained respectively. The conclusion is applied to the ecosystem, it is shown that cross-diffusion can induce the instability of an equilibriumwhich is stable for the kinetic system and for the self-diffusion–reaction system.

AB - In this paper the instability of the uniform equilibrium of a general strongly coupled reaction–diffusion is discussed. In unbounded domain and bounded domain the sufficientconditions for the instability are obtained respectively. The conclusion is applied to the ecosystem, it is shown that cross-diffusion can induce the instability of an equilibriumwhich is stable for the kinetic system and for the self-diffusion–reaction system.

KW - Instability

KW - Cross-diffusion

KW - Pattern formation

U2 - 10.1016/j.nonrwa.2009.01.043

DO - 10.1016/j.nonrwa.2009.01.043

M3 - Journal article

SN - 1468-1218

VL - 11

SP - 1036

EP - 1045

JO - Nonlinear Analysis: Real World Applications

JF - Nonlinear Analysis: Real World Applications

IS - 2

ER -

Instability induced by cross-diffusion in reaction-diffusion systems

Abstract

Keywords

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