The Gellerstedt problem for a parabolic-hyperbolic equation of the 2nd kind

N. K. Mamadaliev

National University of Uzbekistan named after M. Ulugbek

Abstract: In this paper we consider the Gellerstedt problem for a parabolic-hyperbolic equation of the 2nd kind. We prove the unique solvability of this problem, using the representation (obtained by the author) for a solution to the modified Cauchy problem in a generalized class $R$.

Keywords: generalized solution, mixed-type equation, Gellerstedt problem, gluing conditions.

UDC: 517.956

Received: 18.12.2006

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2009, 53:4, 26–30

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