Regularity of the solution of a nonlinear Volterra integral equation of the second kind
type: Item
instance of: scholarly article
title: Regularity of the solution of a nonlinear Volterra integral equation of the second kind
zbMATH Open document ID: 1506.45002
author: H. Liang
author: Martin Stynes
published in: Discrete and Continuous Dynamical Systems. Series B
publication date: 2022-11-23T00:00:00Z
review text: The following nonlinear Volterra integral equation of Urysohn type is discussed: \[ y(t)=g(t)+\int\limits_{0}^{t}K(t,s,y(s))ds, \quad 0\leq t\leq T. \] Here the kernel \(K\) may be smooth or have an integrable singularity and \(g\in C^{m,\beta}(0,T]\) for some positive integer \(m\). The authors study the regularity of the solution \(y\) of this equation. A well-known approach to analyze the smoothness of solutions of such equations consists in reducing them to Fredholm equations and using the corresponding results, see, e.g., [\textit{G. Vainikko}, Multidimensional weakly singular integral equations. Berlin: Springer-Verlag (1993; Zbl 0789.65097)]. Within the framework of Fredholm equations, an alternative method of analysis is proposed.
Mathematics Subject Classification ID: 45D05
Mathematics Subject Classification ID: 45B05
Mathematics Subject Classification ID: 45G05
zbMATH DE Number: 7622300
zbMATH Keywords: Volterra integral equation
zbMATH Keywords: weakly singular kernel
zbMATH Keywords: regularity of solution
reviewed by: Alexander N. Tynda
MaRDI profile type: Publication
full work available at URL: dcdsb.2022164
OpenAlex ID: W4293462118
cites work: Q4067292
cites work: Resolvents and solutions of weakly singular linear Volterra integral equations
cites work: A survey of recent advances in the numerical treatment of Volterra integral and integro-differential equations
cites work: The piecewise polynomial collocation method for nonlinear weakly singular Volterra equations
cites work: The smoothness of solutions to nonlinear weakly singular integral equations
cites work: Multidimensional weakly singular integral equations
DOI: 10.3934/DCDSB.2022164
description: scientific article; zbMATH DE number 7622300