Nonlinear degenerate parabolic equations with Neumann boundary condition
type: Item
instance of: scholarly article
title: Nonlinear degenerate parabolic equations with Neumann boundary condition
zbMATH Open document ID: 1073.35125
author: M. Kubo
author: Quqin Lu
published in: Journal of Mathematical Analysis and Applications
publication date: 2005-06-10T00:00:00Z
review text: The goal of this paper is to give a necessary and sufficient condition for the existence of solutions to the following initial boundary value problem \[ u_t-\Delta v= f(t, x),\;v\in\beta(u)\text{ in }(0,T)\times\Omega,\quad {\partial v\over\partial n}= 0\text{ on }(0,T)\times\partial\Omega,\quad u(0,x)= u_0(x)\text{ in }\Omega,\tag{1} \] where \(\Omega\) is a bounded domain in \(\mathbb{R}^N\), \(N\geq 1\). Under some suitable assumptions of \(f\), \(u_0\) and \(\beta\), the authors present a necessary and sufficient condition for existence of solutions for (1). Existence of solutions for (1) based on three steps: approximation, uniform estimate and limiting process.
Mathematics Subject Classification ID: 35K60
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35A05
zbMATH DE Number: 2174935
zbMATH Keywords: approximation
zbMATH Keywords: uniform estimate
zbMATH Keywords: limiting process
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: j.jmaa.2004.10.052
OpenAlex ID: W1985469294
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DOI: 10.1016/J.JMAA.2004.10.052
description: scientific article; zbMATH DE number 2174935