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Analysis of a semigroup approach in the inverse problem of identifying an unknown coefficient
Author(s) -
Demir Ali,
Ozbilge Ebru
Publication year - 2008
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.989
Subject(s) - semigroup , mathematics , inverse , boundary (topology) , dirichlet boundary condition , function (biology) , inverse problem , dirichlet distribution , mathematical analysis , boundary value problem , pure mathematics , combinatorics , discrete mathematics , geometry , evolutionary biology , biology
This article presents a semigroup approach to the mathematical analysis of the inverse coefficient problems of identifying the unknown coefficient k ( u x ) in the quasi‐linear parabolic equation u t ( x, t )=( k ( u x ) u x ( x, t )) x + F ( x, t ), with Dirichlet boundary conditions u (0, t )=ψ 0 , u (1, t )=ψ 1 and source function F ( x, t ). The main purpose of this paper is to investigate the distinguishability of the input–output mappings Φ[·]: → C 1 [0, T ], Ψ[·]: → C 1 [0, T ] via semigroup theory. Copyright © 2008 John Wiley & Sons, Ltd.