Mathematics

A linear inverse problem for a mixed type operator-differential equation with a parameter

N. L. Abasheieva<sup>ab

a</sup> Sobolev Institute of Mathematics, 4 Koptyug Avenue, Novosibirsk 630090, Russia
^b Novosibirsk State University, 2 Pirogov Street, 2, Novosibirsk 630090, Russia

Abstract: We study the inverse problem
$$Bu_t+pLu=\varphi (t)+f(t, p),\quad u(0, p)=u(T,p)=0.$$
The operators $B,\,L$ are selfadjoint in the Hilbert space $E$ and the spectrum of the operator $L$ is semibounded. The unique solvability of this problem is proved with using a series expansion in eigen and associated elements of the pencil $L-\lambda B.$

Keywords: inverse problem, mixed type equation.

UDC: 517.95

Received: 30.09.2016

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