This article is cited in 25 papers

An inverse problem for an equation of elliptic-hyperbolic type with a nonlocal boundary condition

K. B. Sabitov, N. V. Martem'yanova

Samara State Academy of Social Sciences and Humanities, Samara

Abstract: We examine a mixed type equation with the Lavrent'ev–Bitsadze operator and an unknown right-hand side in a rectangle and study a nonlocal boundary value problem in which the values of the stream function on the lateral sides of the rectangle are equal. The solution is given as a sum of a biorthogonal series. The uniqueness criterion and stability of solutions with respect to the boundary data are established.

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

UDC: 517.95

Received: 11.08.2010

 English version: Siberian Mathematical Journal, 2012, 53:3, 507–519

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