On exact solutions of a class of singular partial integro-differential equations
type: Item
instance of: scholarly article
title: On exact solutions of a class of singular partial integro-differential equations
zbMATH Open document ID: 1468.45006
DOI: 10.1134/S1995080221030240
author: Yanyan Li
published in: Lobachevskii Journal of Mathematics
publication date: 2021-05-20T00:00:00Z
review text: In the modern theory of integro-differential equations, an important topic is the investigation of integro-differential equations with singular and super-singular coefficients. In this work the authors give an integral representation for a solution to a class of second-order partial integro-differential equations with singularities in the kernel. To get this important result, the authors introduce a new class of functions. They prove uniqueness results under suitable conditions and investigate the inverse operators too.
reviewed by: Vincenzo Vespri
Mathematics Subject Classification ID: 45K05
Mathematics Subject Classification ID: 45L05
Mathematics Subject Classification ID: 45Q05
zbMATH DE Number: 7350145
zbMATH Keywords: integro-differential equation
zbMATH Keywords: singular operators
zbMATH Keywords: characteristic equation
zbMATH Keywords: integral representation of manifold solution
zbMATH Keywords: homogeneous equation
Wikidata QID: Q115247352
MaRDI profile type: Publication
cites work: Q3258501
cites work: Q5846646
cites work: Q5576379
cites work: Q5838237
cites work: Singular integro-differential equations of the special type in Banach spaces and its applications
cites work: Degenerate integro-differential equations of convolution type in Banach spaces
cites work: Global solvability of an inverse problem for an integro-differential equation of electrodynamics
cites work: Direct and inverse problems for an operator with nonlocal potential
cites work: Nonlocal boundary value problem for a nonlinear Fredholm integro-differential equation with degenerate kernel
cites work: On inverse boundary value problem for a Fredholm integro-differential equation with degenerate kernel and spectral parameter
cites work: On a boundary-value problem for Boussinesq type nonlinear integro-differential equation with reflecting argument
cites work: The method of normal forms for singularly perturbed systems of Fredholm integro-differential equations with rapidly varying kernels
cites work: Regularized asymptotics of solutions to integro-differential partial differential equations with rapidly varying kernels
cites work: Approximation of solutions to singular integro-differential equations by Hermite - Fejer polynomials
cites work: CONSTRUCTION OF AN ANALOG OF THE FREDHOLM THEOREM FOR A CLASS OF MODEL FIRST ORDER INTEGRO-DIFFERENTIAL EQUATIONS WITH A SINGULAR POINT IN THE KERNEL
cites work: Построение аналога теоремы Фредгольма для одного класса модельных интегро-дифференциальных уравнений первого порядка с логарифмической
full work available at URL: s1995080221030240
OpenAlex ID: W3159292806
description: scientific article; zbMATH DE number 7350145