This article is cited in 33 papers

A nonlocal inverse problem for a mixed-type equation

K. B. Sabitov, N. V. Martem'yanova

Chair of Mathematical Analysis, Volga Region Social-Humanitarian Academy, Samara, Russia

Abstract: We establish a criterion for the unique solvability of the inverse problem for the Lavrent'ev–Bitsadze equation with unknown right-hand member. We construct a solution as the sum of a biorthogonal series over systems of root functions of the corresponding adjoint problems on eigenvalues.

Keywords: mixed-type equation, inverse problem, spectral method, uniqueness, existence.

UDC: 517.956

Received: 30.06.2009

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2011, 55:2, 61–74

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