Existence of a solution for a class of parabolic equations with three unbounded nonlinearities, natural growth terms and L1 data

Arab Journal of Mathematical Sciences

Hicham Redwane¹  Dominique Blanchard² 

[1] Faculté des Sciences Juridiques, Économiques et Sociales, Université Hassan 1, B.P. 764 Settat, Morocco;Laboratoire de Mathématiques Raphaël Salem, UMR 6085, CNRS-Université de Rouen, Avenue de l’Université, BP.12 Technopôle du Madrillet, F76801 Saint-Étienne-du-Rouvray, France;

关键词: Nonlinear parabolic equations;    Existence;    Renormalized solutions;   

DOI  :  10.1016/j.ajmsc.2013.06.002

来源: DOAJ

【 摘 要 】

We give an existence result of a renormalized solution for a class of nonlinear parabolic equations ∂b(x,u)∂t-div(a(x,t,u,∇u))+g(u)|∇u|p=f, where the right side belongs to L1(Ω × (0,T)), b(x,u) is an unbounded function of u and −div(a(x,t,u,∇u)) is a Leray–Lions type operator with growth ∣∇u∣p−1 in ∇u, but without any growth assumption on u. The function g is just assumed to be continuous on R and satisfying a sign condition.

【 授权许可】

Unknown