Existence and Behavior Results For a Nonlocal Nonlinear Parabolic Equation With Variable Exponent

In this paper, we study the solvability of a Cauchy- Dirichlet problem for nonlinear parabolic equation with non standard growths and nonlocal terms. We show the existence of weak solutions of the considered problem under more general conditions. In addition, we obtain some results on the behavior of the solution when the problem is homogeneous.