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

2012/12/06 by M. van den Berg, Peter Gilkey, Berg, M. van den +3 · 1 citation
Computer Science · Mathematics · #35K20 #58J32 #58J35 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1212.1400

openalex publication_date 2012/12/06 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

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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