Uniform Boundedness and Decay Estimates for a System of Reaction-Diffusion Equations with a Triangular Diffusion Matrix on $${\mathbb{R}^{n}}$$

Abstract

This paper concerns with a class of reaction-diffusion systems with triangular diffusion matrix on the unbounded domain \({\mathbb{R}^{n}}\) . The system with diagonal diffusion matrix has been studied by J. D. Avrin and F. Rothe in [4]. We prove two new results about uniform boundedness to solutions of such class of reaction-diffusion systems in \({BUC(\mathbb{R}^{n})}\), the space of bounded uniformly continuous functions from \({\mathbb{R}^{n}}\) to \({\mathbb{R}}\) .