The Inverse Problem for the Heat Equation with Two Unknown Coefficients

We solve the simultaneous recovery of thermal conductivity and a high-frequency coefficient of a sourcein a one-dimensional initial-boundary value problem for the heat equation withDirichlet boundary conditions and an inhomogeneous initial conditionfrom some information on the partial asymptotics of a solution. We showthat the coefficients can be restored from some data on the asymptotics of a solution,which is constructed and justified.This article was inspired by Denisov’s research on a variety of inverseproblems without accounting for high-frequency oscillations.Also, we continue the research by Levenshtam and his students which firstlyaddressed the inverse problems for parabolic equations with high-frequency coefficients and developed the relevantmethodology. In contrast tothe previous research of the case that only the source function or its factors are unknown,we assume that the thermal conductivity and the factor of a source functionare unknown simultaneously.