On the existence of viscosity solutions for the parabolic differential-functional Cauchy problem
type: Item
instance of: scholarly article
title: On the existence of viscosity solutions for the parabolic differential-functional Cauchy problem
zbMATH Open document ID: 1240.35082
published in: Acta Mathematica Hungarica
publication date: 2011-02-25T00:00:00Z
review text: This paper developed solution for nonlinear Cauchy problem for second order differential-functional equations of parabolic type, and provided existence theorems for the class of bounded and in the class of unbounded viscosity solutions. These are based on differential inequalities and on the contraction method. The functional dependence in the equation is of Hale type. The results cover equations with retarded and deviated argument, and differential-integral problems. It is an interesting mathematical paper, the only drawback is that it does not support any formal experiments.
reviewed by: Prabhat Kumar Mahanti
Mathematics Subject Classification ID: 35D40
Mathematics Subject Classification ID: 35K15
Mathematics Subject Classification ID: 35R10
zbMATH DE Number: 5857797
zbMATH Keywords: viscosity solutions
zbMATH Keywords: parabolic equation
zbMATH Keywords: Cauchy problem
zbMATH Keywords: differential-functional equation
author: Krzysztof A. Topolski
MaRDI profile type: Publication
full work available at URL: s10474-010-0029-3
OpenAlex ID: W2078150745
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DOI: 10.1007/S10474-010-0029-3
description: scientific article; zbMATH DE number 5857797