Open AccessExistence of a renormalized solution of nonlinear parabolic equations with general measure data
Author(s) -
Amine Marah,
Hicham Redwane
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.45243
Subject(s) - nabla symbol , omega , measure (data warehouse) , type (biology) , function (biology) , nonlinear system , operator (biology) , mathematics , parabolic partial differential equation , pure mathematics , mathematical physics , combinatorics , mathematical analysis , physics , partial differential equation , chemistry , quantum mechanics , computer science , ecology , biochemistry , repressor , database , evolutionary biology , transcription factor , gene , biology
In this paper we prove the existence of a renormalized solution for nonlinear parabolic equations of the type:$$\displaystyle{\partial b(x,u)\over\partial t} - {\rm div}\Big(a(x,t,\nabla u)\Big)=\mu\qquad \text{in}\ \Omega\times (0,T),$$ where the right handside is a general measure, $b(x,u)$ is anunbounded function of $u$ and $- {\rm div}(a(x,t,\nabla u))$is a Leray--Lions type operator with growth $|\nabla u|^{p-1}$ in$\nabla u$.