Analysis of a semigroup approach in the inverse problem of identifying an unknown coefficient | Zendy

Demir Ali | Zendy; Ozbilge Ebru | Zendy

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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.

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