Open AccessExistence and uniqueness of renormalized solution for nonlinear parabolic equations in Musielak Orlicz spaces
Author(s) -
Ahmed Aberqi,
Jaouad Bennouna,
Mhamed Elmassoudi
Publication year - 2022
Publication title -
boletim da sociedade paranaense de matemática
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.347
H-Index - 15
eISSN - 2175-1188
pISSN - 0037-8712
DOI - 10.5269/bspm.45234
Subject(s) - nabla symbol , uniqueness , type (biology) , nonlinear system , parabolic partial differential equation , order (exchange) , operator (biology) , class (philosophy) , mathematics , pure mathematics , term (time) , mathematical analysis , mathematical physics , physics , partial differential equation , chemistry , quantum mechanics , omega , economics , biology , ecology , biochemistry , finance , repressor , artificial intelligence , gene , transcription factor , computer science
This paper is devoted to the study of a class of parabolic equation of type$$ \frac{\partial u}{\partial t} -div(A(x,t,u,\nabla u) +B(x,t,u)) =f \quad\mbox{in}\quad Q_T, $$where $div(A(x,t,u,\nabla u)$ is a Leray-Lions type operator, $B(x,t,u)$ is a nonlinear lower order term and $f\in L^{1}(Q_{T})$.We show the existence and the uniqueness of renormalized solution in the framework of Musielak-Orlicz spaces.