On the Existence of Mild Solutions of the Initial-Boundary-Value Problems for the Petrovskii-Type Semilinear Parabolic Systems with Variable Exponents of Nonlinearity

Abstract

We study the initial-boundary-value problem with general homogeneous boundary conditions for the Petrovskii-type semilinear parabolic systems with variable exponents of nonlinearity in a cylindrical domain. The existence of mild solutions of this problem is proved.