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Existence and stability of solutions for semi-linear parabolic systems, and applications to some diffusion reaction equations

Synopsis In this paper we study diffusion-reaction equations arising in the theory of chemical reactions. We prove the global existence and uniqueness of a solution without any restriction for the Lewis number and the Biot numbers. In addition, it is shown that there is at least one stationary state which is globally asymptotically stable (in a rather strong sense) provided the Thiele number is sufficiently small. These results are obtained as special cases from much more general results on semilinear parabolic systems, derived below.