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.
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