A class of degenerate totally nonlinear parabolic equations
type: Item
instance of: scholarly article
title: A class of degenerate totally nonlinear parabolic equations
zbMATH Open document ID: 0870.35057
author: Chin-Yuan Lin
author: Li-Chang Fan
published in: Journal of Mathematical Analysis and Applications
publication date: 1997-07-27T00:00:00Z
review text: The following initial-boundary value problem for a degenerate totally nonlinear parabolic equation is considered: \[ u_t=\beta (\phi (x,u_x)u_{xx} + f(x,u,u_x)),\quad (x,t)\in (0,1)\times (0,\infty ), \] \[ u_x(j,t)\in (-1)^j\beta_{j}(u(j,t)),\;j=0,1, \quad u(x,0)=u_0(x), \] as well as its higher space dimensional analogue. Here \(\beta_0\) and \(\beta_1\) are maximal monotone graphs in \(\mathbb{R}\times \mathbb{R},\) and \(\beta (t)\) or \(\beta' (t)\) might equal zero for some \(t.\) It is shown by the method of lines (constructing the Rothe function) and nonlinear semigroup theory that this problem has a unique global solution.
Mathematics Subject Classification ID: 35K60
Mathematics Subject Classification ID: 35R70
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 47H20
zbMATH DE Number: 954714
zbMATH Keywords: fully nonlinear equation
zbMATH Keywords: method of lines
reviewed by: Vladimir N. Grebenev
MaRDI profile type: Publication
full work available at URL: jmaa.1996.0413
OpenAlex ID: W1982625018
DOI: 10.1006/JMAA.1996.0413
description: scientific article; zbMATH DE number 954714