On variations in the solutions of integro-differential equations of mixed problems of elasticity theory for domain variations
type: Item
instance of: scholarly article
title: On variations in the solutions of integro-differential equations of mixed problems of elasticity theory for domain variations
zbMATH Open document ID: 0615.73014
DOI: 10.1016/0021-8928(85)90010-3
author: I. S. Zakharevich
published in: Journal of Applied Mathematics and Mechanics
publication date: 1985-01-01T00:00:00Z
review text: The behaviour of the solution of the boundary value problem for a pseudo- differential equation (PDE), Green's function of this problem, and also some of their local and global characteristics, during variation of the domain is investigated. Formulas are proposed that enable the solution of a broad class of PDE in a domain to be expressed in terms of the solution in the near domain. Local characteristics of the solution are expressed in terms of the local characteristics of the solution in the near domain. A double asymptotic form of Green's function for both arguments tending to the domain boundary occurs in the variational formula. The variation of this double asymptotic form as the domain varies is expressed in terms of this same asymptotic form. The system of variation formulas obtained is closed. It enables the PDE solution in the domain to be reduced to the solution of an ordinary differential equation in functional space. The local characteristics of the solution can also be found by this method without calculating the solution itself. If there is sufficient symmetry in the initial operator, then conservation laws in the Noether sense are obtained for its Green's function and its asymptotic form. The behaviour of the quantities under investigation is studied under inversion.
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 74B99
Mathematics Subject Classification ID: 74H99
Mathematics Subject Classification ID: 35S15
Mathematics Subject Classification ID: 74R05
zbMATH DE Number: 3997238
zbMATH Keywords: Green's function
zbMATH Keywords: global characteristics
zbMATH Keywords: local characteristics
zbMATH Keywords: conservation laws
zbMATH Keywords: Noether sense
MaRDI profile type: Publication
full work available at URL: 0021-8928(85)90010-3
OpenAlex ID: W1978365539
cites work: Q5530582
cites work: Contact problems of the theory of elasticity in the presence of wear
description: scientific article; zbMATH DE number 3997238