The classical solutions for nonlinear parabolic integrodifferential equations
type: Item
instance of: scholarly article
title: The classical solutions for nonlinear parabolic integrodifferential equations
zbMATH Open document ID: 0671.45004
DOI: 10.1216/JIE-1988-1-2-249
author: Hong-Ming Yin
published in: Journal of Integral Equations and Applications
publication date: 1988-01-01T00:00:00Z
review text: The paper deals with the solvability and regularity (in the classical sense) of the initial-boundary value problem for the nonlinear partial integrodifferential equation \[ u_ t=a(x,t,u,u_ x)u_{xx}+b(x,t,u,u_ x)+\int^{t}_{0}c(x,s,u,u_ x)ds, \] \(x\in (0,1)\times (0,T)\); \(u(i,t)=f_ i(t)\), \(t\in [0,T]\), \(i=0,1\); \(u(x,0)=u^ 0(x)\), \(x\in [0,1]\). Uniqueness and continuous dependence of the solution (on the data \(f_ i\), \(u^ 0)\) is also established.
reviewed by: S. D. Milusheva
Mathematics Subject Classification ID: 45K05
Mathematics Subject Classification ID: 45G10
zbMATH DE Number: 4098022
zbMATH Keywords: solvability
zbMATH Keywords: regularity
zbMATH Keywords: initial-boundary value problem
zbMATH Keywords: nonlinear
zbMATH Keywords: Uniqueness
zbMATH Keywords: continuous dependence
MaRDI profile type: Publication
full work available at URL: jie-1988-1-2-249
OpenAlex ID: W2055437427
description: scientific article; zbMATH DE number 4098022