On a Nonlinear Heat Equation Associated with Dirichlet–Robin Conditions
Le Thi Phuong Ngoc, Nguyen Van Y, Alain Pham Ngoc Dinh, Nguyễn Thành Long · Numerical Functional Analysis and Optimization · 2012
This article is devoted to the study 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 t → + ∞. Finally, we give numerical results.