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Existence, stability and smoothness of bounded solutions for an impulsive semilinear system of parabolic equations

Abstract:

In this paper we study the existence, stability and smoothness of bounded solutions for an impulsive semilinear system of parabolic equations with homogeneous Dirichlet boundary condition. Using Banch fixed point theorem, we prove the existence of bounded solutions assuming that the nonlinear terms satisfy a Lipschitz condition, after that, we study the stability and the smoothness of such solutions.