Premium
On an inverse boundary problem for the heat equation when small heat conductivity defects are present in a material
Author(s) -
Bouraoui M.,
Asmi L. El,
Khelifi A.
Publication year - 2016
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201300265
Subject(s) - heat equation , boundary (topology) , inverse problem , bounded function , boundary value problem , mathematical analysis , mathematics , inverse , free boundary problem , poincaré–steklov operator , thermal conductivity , domain (mathematical analysis) , heat kernel , robin boundary condition , physics , thermodynamics , geometry
For the heat equation in a bounded domain we consider the inverse problem of identifying locations and certain properties of the shapes of small heat‐conducting inhomogeneities from dynamic boundary measurements on part of the boundary and for finite interval in time. The key ingredient is an asymptotic method based on appropriate averaging of the partial dynamic boundary measurements. Our approach is expected to lead to very effective computational identification algorithms.