Differential and Integral Equations

Global existence and large time behavior of positive solutions to a reaction diffusion system

Jacob Isaac Kanel and Mokhtar Kirane

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Abstract

We consider a reaction diffusion system whit a triangular matrix of diffusion coefficients satisfying a balance law on a bounded domain with no-flux boundary condition. We demonstrate that globally bounded solutions exist for any reaction term provided a condition on the diffusion coefficients is satisfied. The proof makes use of some properties of the Neumann function for the heat equation posed in a bounded domain recently obtained in [12]. When the spatial domain is {\rm \bf R}$^N$, the proof relies on well-known properties of the fundamental solution of the heat equation.

Article information

Source
Differential Integral Equations Volume 13, Number 1-3 (2000), 255-264.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356124299

Mathematical Reviews number (MathSciNet)
MR1811958

Zentralblatt MATH identifier
1038.35031

Subjects
Primary: 35K57: Reaction-diffusion equations
Secondary: 35B40: Asymptotic behavior of solutions 35K45: Initial value problems for second-order parabolic systems

Citation

Kanel, Jacob Isaac; Kirane, Mokhtar. Global existence and large time behavior of positive solutions to a reaction diffusion system. Differential Integral Equations 13 (2000), no. 1-3, 255--264. https://projecteuclid.org/euclid.die/1356124299.


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