Strongly nonlinear parabolic equations with natural growth terms in Orlicz spaces
type: Item
instance of: scholarly article
title: Strongly nonlinear parabolic equations with natural growth terms in Orlicz spaces
zbMATH Open document ID: 1082.35085
author: A. Elmahi
author: Driss Meskine
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2005-01-11T00:00:00Z
review text: The paper deals with the parabolic initial-boundary value problem \[ \begin{aligned} {\partial u\over\partial t}+ A(u)+ g(t,x,u,\nabla u)= f&\quad\text{in }Q,\\ u(x,t)= 0 &\quad\text{on }\partial\Omega\times (0,T),\\ u(x,0)= u_0(x)&\quad\text{in }\Omega,\end{aligned}\tag{1} \] where \(\Omega\) is a bounded open set in \(\mathbb{R}^N\) \((N\geq 2)\), \(Q= \Omega\times (0,T)\) with \(T> 0\) and \(A(u)= -\text{div}(a(x, t,u\nabla u))\) with \(a: \Omega\times [0, T]\times\mathbb{R}\times\mathbb{R}^N\to \mathbb{R}^N\) a Leray-Lions type operator satisfying some Orlicz space growth conditions. The authors prove the existence of weak solutions for (1) with the nonlinearity \(g\) having ``natural'' growth with respect to the gradient.
reviewed by: Vesa Mustonen
Mathematics Subject Classification ID: 35K60
zbMATH DE Number: 2126022
zbMATH Keywords: Inhomogeneous Orlicz-Sobolev spaces
zbMATH Keywords: Leray-Lions type operator
MaRDI profile type: Publication
full work available at URL: j.na.2004.08.018
OpenAlex ID: W2024507082
cites work: Q4073917
cites work: Almost everywhere convergence of the gradients of solutions to elliptic equations in Orlicz spaces and application
cites work: Q3482198
cites work: Almost everywhere convergence of the gradients of solutions to elliptic and parabolic equations
cites work: Strongly nonlinear parabolic initial-boundary value problems
cites work: Nonlinear parabolic equations with natural growth conditions and L1 data
cites work: Inhomogeneous Orlicz-Sobolev spaces and nonlinear parabolic initial value problems
cites work: Q4547353
cites work: Q4806995
cites work: Parabolic Equations in Orlicz Spaces
cites work: Nonlinear Elliptic Boundary Value Problems for Equations With Rapidly (Or Slowly) Increasing Coefficients
cites work: Some approximation properties in Orlicz-Sobolev spaces
cites work: Variational inequalities in Orlicz-Sobolev spaces
cites work: Q4139197
cites work: On the existence of weak solutions for quasilinear parabolic initial-boundary value problems
cites work: A strongly nonlinear parabolic initial boundary value problem
cites work: On parabolic initial-boundary value problems with critical growth for the gradient
cites work: Q5890172
cites work: Inéquations variationnelles paraboliques fortement non linéaires
cites work: Compact sets in the space \(L^ p(0,T;B)\)
DOI: 10.1016/J.NA.2004.08.018
description: scientific article; zbMATH DE number 2126022