Viscosity solutions of fully nonlinear parabolic systems.
type: Item
instance of: scholarly article
title: Viscosity solutions of fully nonlinear parabolic systems.
zbMATH Open document ID: 1036.35079
DOI: 10.1016/S0022-247X(03)00108-2
author: Yin Yang
author: Gang Lü
author: Weian Liu
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-07-30T00:00:00Z
review text: The authors prove the existence, uniqueness and continuity of viscosity solutions of the Cauchy-Dirichlet problem for weakly coupled, nonlinear, second order, degenerate parabolic equations. The proof uses the Perron method in combination with the technique of coupled sub and super viscosity solutions. The results are a generalization of previous work of \textit{H. Engler} and \textit{S. M. Lenhart} [Proc. Lond. Math. Soc. (3) 63, 212--240 (1991; Zbl 0704.35030)] for systems of first order Hamilton-Jacobi equations, and of \textit{H. Ishii} and \textit{S. Koike} [Commun. Partial Differ. Equations 16, 1095--1128 (1991; Zbl 0742.35022)] for monotone systems of fully nonlinear second order elliptic equations.
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35K15
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35B50
Mathematics Subject Classification ID: 35D05
zbMATH DE Number: 1956867
zbMATH Keywords: Cauchy-Dirichlet problem
zbMATH Keywords: Perron method
reviewed by: John Urbas
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1956867