This article is cited in 21 papers

Inverse problem for degenerate parabolic-hyperbolic equation with nonlocal boundary condition

K. B. Sabitov^a, S. N. Sidorov<sup>b

a</sup> Laboratory of Differential Equations, Institute of Applied Research of Bashkortostan Republic, 68 Odesskaya str., Sterlitamak, 453103 Russia
^b Chair of Mathematical Analysis, Sterlitamak Branch of the Bashkir State University, 37 Lenin Ave., Sterlitamak, 453103 Russia

Abstract: For a mixed type equation with a power-law degeneration we consider the inverse problem on finding an unknown right side. We establish a uniqueness criterion of solution to the problem with a nonlocal condition that connects the normal derivative of the sought-for solution, which belongs to different types of studied equations. The solution is constructed in the form of sums of a series in eigenfunctions of the corresponding one-dimensional spectral problem. We also prove stability of the solution to the non-local boundary condition.

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

UDC: 517.957

Received: 27.09.2013

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2015, 59:1, 39–50

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