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Existence of Renormalized Solutions for Nonlinear Parabolic Equations

Existence of Renormalized Solutions for Nonlinear Parabolic Equations
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Year:    2014

Author:    Youssef Akdim, Hicham Redwane, A. Benkirane, M. EL Moumni, Hicham Redwane

Journal of Partial Differential Equations, Vol. 27 (2014), Iss. 1 : pp. 28–49

Abstract

We give an existence result of a renormalized solution for a class of nonlinear parabolic equations $$\frac{\partial b(x,u)}{\partial t}-div(a(x,t,u,\nabla u))+g(x,t,u,\nabla u)+H(x,t,\nabla u)=f,\qquad in\; Q_T,$$ where the right side belongs to $L^{p'}(0,T;W^{-1,p'}(Ω))$ and where b(x,u) is unbounded function of u and where $-div(a(x,t,u,∇u))$ is a Leray-Lions type operatorwith growth $|∇u|^{p-1}$ in ∇u. The critical growth condition on g is with respect to ∇u and no growth condition with respect to u, while the function $H(x,t,∇u)$ grows as $|∇u|^{p-1}$.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jpde.v27.n1.2

Journal of Partial Differential Equations, Vol. 27 (2014), Iss. 1 : pp. 28–49

Published online:    2014-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    22

Keywords:    Nonlinear parabolic equations

Author Details

Youssef Akdim

Hicham Redwane

A. Benkirane

M. EL Moumni

Hicham Redwane

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