Existence and decay of global solutions of some nonlinear degenerate parabolic equations
type: Item
instance of: scholarly article
title: Existence and decay of global solutions of some nonlinear degenerate parabolic equations
zbMATH Open document ID: 0584.35062
DOI: 10.1016/0022-247X(85)90180-5
author: Mitsuhiro Nakao
published in: Journal of Mathematical Analysis and Applications
publication date: 1985-01-01T00:00:00Z
review text: The paper is concerned with the initial-boundary value problem: \[ u_ t-\Delta (| u|^ mu)+\nabla \cdot (g_ 1(u),g_ 2(u),...,g_ n(u))+h(u)=0\quad on\quad \Omega \times R^+,\quad u(x,0)=u_ 0,\quad u|_{\partial \Omega}=0, \] where \(m\geq 0\), \(\Omega\) is a bounded domain of \(R^ n\) with smooth boundary \(\partial \Omega\). Its object is to show that a modified method of potential well can be applied, and a global solution exists if the initial value \(u_ 0\) is small in a certain sense; a decay estimate of such solutions as t tends to infinity is also derived. A uniqueness result is given for \(m=0\).
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35K60
Mathematics Subject Classification ID: 35K20
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35A07
zbMATH DE Number: 3935606
zbMATH Keywords: nonlinear degenerate parabolic equation
zbMATH Keywords: initial-boundary value problem
zbMATH Keywords: method of potential well
zbMATH Keywords: global solution
zbMATH Keywords: decay estimate
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3935606