This article is cited in 44 papers

The inverse problem for a mixed-type parabolic-hyperbolic equation in a rectangular domain

K. B. Sabitov^a, E. M. Safin<sup>b

a</sup> Laboratory of Differential Equations, Academy of Sciences of the Republic of Bashkortostan, Sterlitamak Branch, Sterlitamak, Russia
^b Department of Differential Equations, Institute of Mathematics with Computing Center, Ufa Scientific Center, Russian Academy of Sciences, Ufa, Russia

Abstract: In this paper with the help of the spectral method we obtain a criterion for the unique solvability of the inverse problem for a mixed-type parabolic-hyperbolic equation in a rectangular domain. This problem implies the search of the unknown right-hand side.

Keywords: spectral method, Fourier series, inverse problem, mixed-type parabolic-hyperbolic equation.

UDC: 517.957

Received: 25.12.2007

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2010, 54:4, 48–54

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