Analysis for the identification of an unknown diffusion coefficient via semigroup approach | Zendy

Demir Ali | Zendy; Ozbilge Ebru | Zendy

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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.

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