CLOAKING VIA MAPPING FOR THE HEAT EQUATION
CLOAKING VIA MAPPING FOR THE HEAT EQUATION
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DOI：
10.1137/17m1161452
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发表时间：
2018-01-01
影响因子：
1.6
通讯作者：
Pavliotis, G. A.
中科院分区：
文献类型：
--
作者：
Craster, R. V.;Guenneau, S. R. L.;Pavliotis, G. A.
本文探讨的概念，近隐身的背景下，随时间变化的热传播。我们表明，经过一定的阈值时间，边界测量的齐次热方程接近隐形热问题在一定的Sobolev空间范数，而不管在隐形区域的密度-电导率对。正则化变换介质理论来达到我们的结果。我们的证明依赖于对具有高密度和高电导率系数的抛物问题的解的长时间行为的研究。它进一步依赖于在稳态传导问题的背景下存在小缺陷的边界测量估计的研究。然后，我们提出了一些数值例子来说明我们的理论结果。
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 measurements 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 regularized transformation media theory is employed to arrive at our results. Our proof relies on the study of the long time behavior 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 problems. We then present some numerical examples to illustrate our theoretical results.