Article

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

  • M. van den BergAffiliated withSchool of Mathematics, University of Bristol
  • , P. GilkeyAffiliated withMathematics Department, University of Oregon Email author 
  • , H. KangAffiliated withDepartment of Mathematics, Korea Institute for Advanced Study

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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

58J32 58J35 35K20

Keywords

Neumann Laplacian heat content asymptotics singular initial temperature