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Neumann heat content asymptotics with singular initial temperature and singular specific heat |
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| Authors: | M van den Berg P Gilkey H Kang |
| Institution: | 1. School of Mathematics, University of Bristol, University Walk, Bristol, BS8 1TW, United Kingdom 2. Mathematics Department, University of Oregon, Eugene, OR, 97403, USA 3. Department of Mathematics, Korea Institute for Advanced Study, 87 Hoegiro Dongdaemun-gu, Seoul, 130-722, Korea |
| 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. |
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