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Exponentially-bounded solutions of a system of parabolic equations

Abstract:

In this article we study the existence of exponentially-bounded solutions of the following non-linear system of parabolic equations with homogeneous Neumann boundary conditions (Formula presented.) where (Formula presented.) is a diagonal matrix with (Formula presented.) and Ω is a bounded domain in (Formula presented.). Under some conditions we prove the existence of a continuous manifold such that any solution with initial condition in this manifold is exponentially bounded. © 2004, Taylor & Francis Group, LLC.