We consider a class of reaction-diffusion systems with macroscopic convection and nonlinear diffusion plus a nonstandard boundary condition which results as a model for heterogeneous catalysis in a stirred multiphase chemical reactor. Since the appearance of T-periodic feeds is a common feature in such applications, we study the problem of existence of a T-periodic solution. The model under consideration admits an abstract formulation in an appropriate L~1-setting, which leads to an evolution problem of the type u' + Au imply f(t, u) on R_+. Here A is an m-accretive operator in a Banach space X and f:R_+ * K → X is T-periodic and of Caratheodory type where K is a closed, bounded, convex subset of X. Sufficient conditions on A, f and K to assure existence of T-periodic mild solutions for this evolution problem are provided and applied to the class of reaction-diffusion systems mentioned above.
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