ARTICLE
Renormalized solutions for convection-diffusion problems involving a nonlocal operator
- Nonlinear Differential Equations and Applications NoDEA , 28 : 1-27
Lien de l'article :
https://doi.org/10.1007/s00030-021-00713-8
Discipline :
Mathématiques, Physique, Chimie et Informatique
Auteur(s) :
Adama Ouédraogo, Dofyniwassouani Alain Houede, Idrissa Ibrango
Auteur(s) tagués :
HOUEDE Dofyniwassouani Alain
Renseignée par : HOUEDE Dofyniwassouani Alain
Résumé
The aim of this paper is to establish an L1-well-posedness theory
in the sense of renormalized entropy solution for anisotropic diffusion-
convection problems involving a nonlocal diffusion operator. Our strategy
is to follow the approach developed in Bendahmane and Karlsen (SIAM
J Math Anal, 36(2):405–422, 2004) to generalize the existence and the
uniqueness results of Karlsen and Ulusoy (J Differ Equ 116:1–23, 2011)
to the class of integrable initial data with a term source depending on the
unknown function u.
Mots-clés
existence and uniqueness of solutions