In this section
@article{Craster:2018:10.1137/17M1161452,
author = {Craster, R and Guenneau, S and Hutridurga, Ramaiah H and Pavliotis, G},
doi = {10.1137/17M1161452},
journal = {Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal},
pages = {1146--1174},
title = {Cloaking via mapping for the heat equation},
url = {http://dx.doi.org/10.1137/17M1161452},
volume = {16},
year = {2018}
}
TY - JOUR
AB - This paper explores the concept of near-cloaking in the context of time-dependentheat 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 Sobolevspace 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 longtime behaviour of solutions to the parabolic problems with high contrast in density and conductivitycoefficients. It further relies on the study of boundary measurement estimates in the presence of smalldefects in the context of steady conduction problem. We then present some numerical examples to illustrate our theoretical results.
AU - Craster,R
AU - Guenneau,S
AU - Hutridurga,Ramaiah H
AU - Pavliotis,G
DO - 10.1137/17M1161452
EP - 1174
PY - 2018///
SN - 1540-3459
SP - 1146
TI - Cloaking via mapping for the heat equation
T2 - Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal
UR - http://dx.doi.org/10.1137/17M1161452
UR - http://hdl.handle.net/10044/1/59114
VL - 16
ER -