Nonlinear equations with unbounded heat conduction and integrable data

Dominique Blanchard (1, 2) , Olivier Guibé (2) , Hicham Redwane (3)

1 LJLL - Laboratoire Jacques-Louis Lions
2 LMRS - Laboratoire de Mathématiques Raphaël Salem
3 Faculté de Sciences Juridiques, Economiques et Sociales [Settat]

We consider a class of quasi-linear diffusion problems involving a matrix A(t, x, u) which blows up for a finite value m of the unknown u. Stationary and evolution equations are studied for L1 data. We focus on the case where the solution u can reach the value m. For such problems we introduce a notion of renormalized solutions and we prove the existence of such solutions.

Domaines: Analyse fonctionnelle [math.FA]

Dominique Blanchard, Olivier Guibé, Hicham Redwane. Nonlinear equations with unbounded heat conduction and integrable data. 2006. ⟨hal-00112599⟩