This article is cited in 25 papers

Boundary-Value Problem with Nonlocal Integral Condition for Mixed-Type Equations with Degeneracy on the Transition Line

Yu. K. Sabitova<sup>ab

a</sup> Sterlitamak branch of Bashkir State University
^b Institute of Applied Research, Sterlitamak

Abstract: For an elliptic-hyperbolic type equation, the boundary-value problem with nonlocal Samarskii–Ionkin condition in a rectangular domain is solved. Using the spectral analysis method, a uniqueness criterion is established and the existence theorem for the solution of the problem is proved. The solution of the problem is constructed as the sum of a biorthogonal series.

Keywords: elliptic-hyperbolic type equation, boundary-value problem, Samarskii–Ionkin condition, spectral analysis, Bessel's equation, Weierstrass criterion.

UDC: 517.95

Received: 01.05.2011
Revised: 03.03.2015

DOI: 10.4213/mzm9135

 English version: Mathematical Notes, 2015, 98:3, 454–465

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