This article is cited in 13 papers

The boundary-value problem for the Lavrent'ev–Bitsadze equation with unknown right-hand side

K. B. Sabitov^a, I. A. Khadzhi<sup>b

a</sup> Laboratory of Differential Equations, Institute of Applied Research of Academy of Sciences of Republic Bashkortostan, Sterlitamak, Russia
^b Chair of Mathematical Analysis, Sterlitamak State Pedagogical Academy, Sterlitamak, Russia

Abstract: We study the inverse problem for the Lavrent'ev–Bitsadze equation in a rectangular domain. We construct its solution as a series in eigenfunctions for the corresponding problem on eigenvalues and establish a criterion for its uniqueness. We also prove the stability of the obtained solution.

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

UDC: 517.95

Received: 03.11.2009

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2011, 55:5, 35–42

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