Influence of variable coefficients on global existence of solutions of semilinear heat equations with nonlinear boundary conditions

Alexander Gladkov , Mohammed Guedda (1)

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352

We consider semilinear parabolic equations with nonlinear boundary conditions. We give conditions which guarantee global existence of solutions as well as blow-up in finite time of all solutions with nontrivial initial data. The results depend on the behavior of variable coefficients as t -> infinity.

Domaines: Mathématiques [math]

Alexander Gladkov, Mohammed Guedda. Influence of variable coefficients on global existence of solutions of semilinear heat equations with nonlinear boundary conditions. Electronic Journal of Qualitative Theory of Differential Equations, 2020, 63, pp.1-11. ⟨10.14232/ejqtde.2020.1.63⟩. ⟨hal-03621259⟩