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Analysis for the identification of an unknown diffusion coefficient via semigroup approach
Author(s) -
Demir Ali,
Ozbilge Ebru
Publication year - 2009
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.1141
Subject(s) - semigroup , mathematics , dirichlet boundary condition , boundary (topology) , diffusion , function (biology) , dirichlet distribution , mathematical analysis , heat equation , inverse , boundary value problem , pure mathematics , discrete mathematics , combinatorics , geometry , thermodynamics , physics , evolutionary biology , biology
This paper presents a semigroup approach for the mathematical analysis of the inverse coefficient problems of identifying the unknown coefficient k ( u x ) in the inhomogenenous quasi‐linear parabolic equation u t ( x , t )=( k ( u x ) u x ( x , t )) x + F ( u ), with the Dirichlet boundary conditions u (0, t )=ψ 0 , u (1, t )=ψ 1 and source function F ( u ). 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 © 2009 John Wiley & Sons, Ltd.