On a nonlinear heat equation associated with Dirichlet -- Robin conditions

This paper is devoted to the study of a nonlinear heat equation associated with Dirichlet-Robin conditions. At first, we use the Faedo -- Galerkin and the compactness method to prove existence and uniqueness results. Next, we consider the properties of solutions. We obtain that if the initial condition is bounded then so is the solution and we also get asymptotic behavior of solutions as. Finally, we give numerical results