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Neumann heat content asymptotics with singular initial temperature and singular specific heat. (English) Zbl 1311.58015
The authors 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. By assuming the existence of a complete asymptotic series they determine the first three terms in that series. Recursion relations among the coefficients of that series and the relationship between the Dirichlet and Robin settings are studied in detail.

MSC:
58J32 Boundary value problems on manifolds
58J37 Perturbations of PDEs on manifolds; asymptotics
58J35 Heat and other parabolic equation methods for PDEs on manifolds
35K20 Initial-boundary value problems for second-order parabolic equations
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