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.
Citation
Jacob Isaac Kanel. Mokhtar Kirane. "Global existence and large time behavior of positive solutions to a reaction diffusion system." Differential Integral Equations 13 (1-3) 255 - 264, 2000. https://doi.org/10.57262/die/1356124299
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