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

Le Thi Phuong Ngoc (1) , Nguyen van y (2) , Alain Pham Ngoc Dinh (3) , Nguyen Thanh Long (2)

1 Mathematics department
2 UNS-HCMC - University of Natural Science, Vietnam National University HoChiMinhCity
3 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

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

Mots clés: Asymptotic behavior of the solution; Faedo; Galerkin method; nonlinear heat equation; Robin conditions

Domaines: Equations aux dérivées partielles [math.AP]

Le Thi Phuong Ngoc, Nguyen van y, Alain Pham Ngoc Dinh, Nguyen Thanh Long. On a nonlinear heat equation associated with Dirichlet -- Robin conditions. 2010. ⟨hal-00528233⟩