Cloaking via mapping for the heat equation

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Title: Cloaking via mapping for the heat equation
Author(s): Craster, R
Guenneau, S
Hutridurga Ramaiah, H
Pavliotis, G
Item Type: Journal Article
Abstract: This paper explores the concept of near-cloaking in the context of time-dependent heat propagation. We show that after the lapse of a certain threshold time, the boundary measure- ments for the homogeneous heat equation are close to the cloaked heat problem in a certain Sobolev space norm irrespective of the density-conductivity pair in the cloaked region. A regularised trans- formation media theory is employed to arrive at our results. Our proof relies on the study of the long time behaviour of solutions to the parabolic problems with high contrast in density and conductivity coefficients. It further relies on the study of boundary measurement estimates in the presence of small defects in the context of steady conduction problem. We then present some numerical examples to illustrate our theoretical results.
Publication Date: 1-Jan-2018
Date of Acceptance: 13-Apr-2018
ISSN: 1540-3459
Publisher: Society for Industrial and Applied Mathematics
Journal / Book Title: Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/L020564/1
Copyright Statement: This paper is embargoed until publication. Once published it will be available fully open access.
Keywords: 0102 Applied Mathematics
Applied Mathematics
Publication Status: Accepted
Embargo Date: publication subject to indefinite embargo
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences

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