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Recovery of an unknown specific heat by means of overposed data
Author(s) -
Pilant Michael,
Rundell William
Publication year - 1990
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.1690060102
Subject(s) - mathematics , convergence (economics) , inverse problem , mathematical analysis , boundary value problem , heat equation , function (biology) , inverse , dirichlet distribution , class (philosophy) , extension (predicate logic) , geometry , evolutionary biology , artificial intelligence , computer science , programming language , economics , biology , economic growth
In this paper we consider a class of inverse problems in which an unknown function, c (.), is to be determined from a parabolic initial‐value problem, with overposed Dirichlet data along a portion of the boundary. A mapping between the overposed data and the unknown coefficient is obtained in the form of a singular integral equation. This is solved by iteration, and the resulting fixed point is shown to be the solution of the inverse problem. Sufficient conditions for convergence of this method, as well as an extension to the case of an unknown thermal conductivity, are given.