  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
