Uniqueness in one inverse problem of memory reconstruction (Q1358038)

The authors consider the Cauchy problem for an integro-partial differential equation describing wave propagation in \(\mathbb R^3\) with memory caused by a point source. The corresponding inverse problem is to recover the integral kernel in the equation when some information is available on the scattered wave. Using the method of \textit{M. M. Lavrent'ev} [Sov. Math., Dokl. 6, 29--32 (1965); translation from Dokl. Akad. Nauk SSSR 160, 32--35 (1965; Zbl 0141.10203)], a uniqueness theorem is proved for the solution of the inverse problem.