Existence and non-existence of global solutions to initial boundary value problems for nonlinear evolution equations with the strong dissipation

Akisato Kubo (1) , Jean-Pierre Lohéac (2, 3)

1 Department of Mathematics, School of Health Sciences
2 ICJ - Institut Camille Jordan
3 ISCP - Interdisciplinary Scientific Center Poncelet

The main purpose in this paper is to investigate existence and non-existence of global solutions of the initial Dirichlet-boundary value problem for evolution equations with the strong dissipation. Many authors studied some classes consisting of such type of equations for which initial boundary value problems possess global solutions. For this purpose we consider a related problem and seek global solutions ans blow-up solutions depending on whether it belongs to such classes or not.

Mots clés: evolution equation; strong dissipation; blow-up; global existence

Domaines: Equations aux dérivées partielles [math.AP]

Akisato Kubo, Jean-Pierre Lohéac. Existence and non-existence of global solutions to initial boundary value problems for nonlinear evolution equations with the strong dissipation. 2009. ⟨hal-00361333⟩