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Direct and inverse asymptotic problems with high-frequency terms. (English) Zbl 1342.35387

Summary: This paper is devoted to the first boundary value problem for the heat equation with a fast oscillating source. Direct and inverse problems are solved. The direct problem is to construct and justify an asymptotic expansion for the solution under appropriate assumptions. The inverse problem is to find the source if the value of two-term asymptotic expansion for solution at some point of space is given.

MSC:

35Q79 PDEs in connection with classical thermodynamics and heat transfer
80A20 Heat and mass transfer, heat flow (MSC2010)
80A23 Inverse problems in thermodynamics and heat transfer
35R30 Inverse problems for PDEs
35C20 Asymptotic expansions of solutions to PDEs
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References:

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