Blow-up results for a semilinear parabolic differential inequality in an exterior domain

Article type: Research Article

Authors: Jleli, Mohamed | Samet, Bessem^{; *}

Affiliations: Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia. E-mails: [email protected], [email protected]

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: We are concerned with a semilinear parabolic differential inequality posed in an exterior domain of RN, N⩾3. Some blow-up and existence results are established for the considered problem. The novetly of this paper lies in considering a nontrivial Dirichlet boundary condition, which depends both on time and space. Indeed, to the best of our knowledge, in all articles which deal with the blow-up of solutions in exterior domains, the considered boundary condition is trivial or depends only on space.

Keywords: Blow-up, exterior domain, nontrivial Dirichlet boundary condition

DOI: 10.3233/ASY-191555

Journal: Asymptotic Analysis, vol. 118, no. 1-2, pp. 35-47, 2020