Perturbation method for abstract second-order inverse problems

We are concerned with an abstract second-order inverse problem. We restrict ourselves here to abstract inverse problems in which, in order to solve the differential equation for u ( t ) , it is necessary to know the value of some operator or functional ϕ [ u ( t ) ] = g ( t ) as a function of the ar...

Full description

Saved in:
Bibliographic Details
Published in:Nonlinear analysis Vol. 72; no. 3; pp. 1379 - 1386
Main Author: Awawdeh, Fadi
Format: Journal Article
Language:English
Published: Amsterdam Elsevier Ltd 01.02.2010
Elsevier
Subjects:
Exact sciences and technology
Inverse problem
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis in abstract spaces
Numerical analysis. Scientific computation
Operator theory
Ordinary differential equations
Perturbation theory of linear operators
Sciences and techniques of general use
Semigroup of linear operators
47A55
34G99
Semigroup of linear operators
Perturbation theory of linear operators
34A55
Inverse problem
Perturbation theory
Second order equation
Existence condition
Operator semigroup
Differential equation
Existence of solution
Nonlinear analysis
Linear operator
Perturbation method
Sufficient condition
Elasticity theory
Mathematical model
ISSN:0362-546X, 1873-5215
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We are concerned with an abstract second-order inverse problem. We restrict ourselves here to abstract inverse problems in which, in order to solve the differential equation for u ( t ) , it is necessary to know the value of some operator or functional ϕ [ u ( t ) ] = g ( t ) as a function of the argument t . A new approach based on the perturbation theory of linear operators is introduced. Among the results obtained we point out sufficient conditions of existence and uniqueness of a solution. As a possible application of the abstract theorems, some applications from elasticity theory are given.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2009.08.021