Nonlinear Volterra equation of parabolic type due to singular kernels
type: Item
instance of: scholarly article
title: Nonlinear Volterra equation of parabolic type due to singular kernels
zbMATH Open document ID: 0817.45010
author: Gustaf Gripenberg
published in: Journal of Differential Equations
publication date: 1995-08-13T00:00:00Z
review text: The author studies an integral equation of the form \[ u_ t (t,x) = \int^ t_ 0 k(t - s) \bigl( \sigma (u_ x) \bigr)_ x (s,x)ds + f(t,x) \] with a nonincreasing convex kernel \(k\) and \(\sigma\) increasing. Such equations occur in viscoelasticity. Sufficient conditions for the global existence of a strong solution are given. Sufficiently smooth solutions will be unique.
Mathematics Subject Classification ID: 45K05
Mathematics Subject Classification ID: 45G05
Mathematics Subject Classification ID: 74Hxx
zbMATH DE Number: 635869
zbMATH Keywords: nonlinear Volterra equation of parabolic type
zbMATH Keywords: singular kernels
zbMATH Keywords: nonincreasing convex kernel
zbMATH Keywords: viscoelasticity
zbMATH Keywords: strong solution
zbMATH Keywords: smooth solutions
reviewed by: J.Schoenenberger-Deuel
MaRDI profile type: Publication
full work available at URL: jdeq.1994.1098
OpenAlex ID: W2095372802
DOI: 10.1006/JDEQ.1994.1098
description: scientific article; zbMATH DE number 635869