Direct and inverse asymptotic problems with high-frequency terms

Article type: Research Article

Authors: Babich, P.V.^a | Levenshtam, V.B.^{a; b; *}

Affiliations: [a] Southern Federal University, Rostov-on-Don, Russia | [b] Southern Mathematical Institute of the Vladikavkaz, Rostov-on-Don, Russia

Correspondence: [*] Corresponding author. E-mail: vleven@math.rsu.ru.

Abstract: 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.

Keywords: asymptotics, heat equation, high-frequency, inverse problem

DOI: 10.3233/ASY-161356

Journal: Asymptotic Analysis, vol. 97, no. 3-4, pp. 329-336, 2016