On the local behavior of solutions of singular parabolic equations
type: Item
instance of: scholarly article
title: On the local behavior of solutions of singular parabolic equations
zbMATH Open document ID: 0673.35047
DOI: 10.1007/BF00251444
author: Emmanuele DiBenedetto
author: Ya Zhe Chen
published in: Archive for Rational Mechanics and Analysis
publication date: 1988-01-01T00:00:00Z
review text: Soit \(\Omega\) un ensemble en \(R^ N\), \(0<T<\infty\), \(\Omega_ T\equiv \Omega \times (0,T)\), \(u=u(x,t)\). On étudie l'équation \[ (1)\quad u_ t-div a(x,u,Du)+b(x,t,u,Du)=0, \] où Du est le gradient seulement dans les variables d'espace \(x\equiv (x_ 1,x_ 2,...,x_ N)\). Les fonctions a: \(R^{2N+1}\to R^ N\), b: \(R^{2N+2}\to R^ N\) sont mesurables et satisfont conditions, pour lesquelles ont renvoit au mémoire. On étudie solutions faibles de l'équation (1) (supersolutions et subsolutions): \[ u\in V_{2p}(\Omega_ T)\equiv C(0,T,L^ 2(\Omega))\cap L^ 2(0,T,H^ p(\Omega)). \]
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35D05
zbMATH DE Number: 4101716
zbMATH Keywords: singular
zbMATH Keywords: measurable nonlinearity
zbMATH Keywords: weak solution
zbMATH Keywords: sub- and
zbMATH Keywords: super- solution
reviewed by: Maria Cinquini-Cibrario
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00251444
OpenAlex ID: W1993316673
description: scientific article; zbMATH DE number 4101716