Study of solutions to a class of certain parabolic systems with variable exponents

Abstract

-In this paper, the authors study an initial and boundary value problem to a system of evolution p(x)-Laplacian systems coupled with general nonlinear terms:The authors translate the parabolic equation into the elliptic equation by using the time discretization method, and then the existence and uniqueness solution are obtained. The blow-up results is shown, by using the energy method.