Premium
Simultaneous reconstruction of the source term and the surface heat transfer coefficient
Author(s) -
Kaya Mujdat,
Erdem Arzu
Publication year - 2015
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.3084
Subject(s) - mathematics , lipschitz continuity , monotone polygon , term (time) , constant (computer programming) , dirichlet distribution , boundary (topology) , inverse problem , mathematical analysis , constant coefficients , surface (topology) , boundary value problem , geometry , computer science , physics , quantum mechanics , programming language
We study the problem of identifying unknown source terms in an inverse parabolic problem, when the overspecified (measured) data are given in form of Dirichlet boundary condition u (0, t ) = h ( t ) and u ( x , t ) = q ( x , t ) ,( x , t ) ∈ Ω °t 1, where Ω °t 1is an arbitrarily prescribed subregion. The main goal here is to show that the gradient of cost functional can be expressed via the solutions of the direct and corresponding adjoint problems. We prove Hölder continuity of the cost functional and derive the Lipschitz constant in the explicit form via the given data. On the basis of the obtained results, we propose a monotone iteration process. Copyright © 2014 John Wiley & Sons, Ltd.