Journal of Fixed Point Theory and Applications

, Volume 14, Issue 1, pp 267–298

Neumann heat content asymptotics with singular initial temperature and singular specific heat

Article

DOI: 10.1007/s11784-013-0147-y

Cite this article as:
van den Berg, M., Gilkey, P. & Kang, H. J. Fixed Point Theory Appl. (2013) 14: 267. doi:10.1007/s11784-013-0147-y
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Abstract

We study the asymptotic behavior of the heat content on a compact Riemannian manifold with boundary and with singular specific heat and singular initial temperature distributions imposing Robin boundary conditions. Assuming the existence of a complete asymptotic series we determine the first three terms in that series. In addition to the general setting, the interval is studied in detail as are recursion relations among the coefficients and the relationship between the Dirichlet and Robin settings.

Mathematics Subject Classification

58J3258J3535K20

Keywords

Neumann Laplacianheat content asymptoticssingular initial temperature

Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.School of MathematicsUniversity of BristolBristolUnited Kingdom
  2. 2.Mathematics DepartmentUniversity of OregonEugeneUSA
  3. 3.Department of MathematicsKorea Institute for Advanced StudySeoulKorea