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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Asymptotic analysis of a Dirichlet problem for the heat equation on a coated body
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by Jingyu Li, Steve Rosencrans, Xuefeng Wang and Kaijun Zhang PDF
Proc. Amer. Math. Soc. 137 (2009), 1711-1721 Request permission

Abstract:

Of concern is the protection from overheating of an isotropically conducting body by an anisotropically conducting coating which is thin compared to the scale of the body. We assume either that the whole thermal tensor of the coating is small or that it is small in the directions normal to the body (a case we call “optimally aligned coating”). We study the asymptotic behavior of the solution to the heat equation with Dirichlet boundary conditions on the outer surface of the coating, as the thickness of the coating shrinks. We obtain the exact scaling relations between the thermal tensor and the thickness of the coating so that the effective (limiting) condition on the boundary of the body is of Dirichlet, Robin or Neumann type, with the last condition indicating good insulation.
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Additional Information
  • Jingyu Li
  • Affiliation: School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, People’s Republic of China
  • Email: lijy645@yahoo.com.cn
  • Steve Rosencrans
  • Affiliation: Department of Mathematics, Tulane University, New Orleans, Louisiana 70118
  • Email: srosenc@tulane.edu
  • Xuefeng Wang
  • Affiliation: Department of Mathematics, Tulane University, New Orleans, Louisiana 70118
  • Email: xdw@math.tulane.edu
  • Kaijun Zhang
  • Affiliation: School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, People’s Republic of China
  • Email: zhangkj201@nenu.edu.cn
  • Received by editor(s): May 19, 2008
  • Published electronically: December 11, 2008
  • Communicated by: Walter Craig
  • © Copyright 2008 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 137 (2009), 1711-1721
  • MSC (2000): Primary 35K05, 35K20, 35R05, 80A20, 80M35
  • DOI: https://doi.org/10.1090/S0002-9939-08-09766-9
  • MathSciNet review: 2470829