ICM 1998, Berlin, Aug. 18 – 27

Abstract of Short Communications and Posters

Section:

10. Partial Differential Equations

1991 MS Classification: 34, 35 Mamadaliev, Nasirjan, Tashkent State University, Rep. Uzbekistan The Problem of Gellerstedt for a secondking equation of the parabolichyperbolic type We consider the equation of fixed type α = −n+α_{0}, 0.5 < α_{0} < 0, 0 < α_{0} < 0.5

0 = \{ \begin{matrix}xu_{xx} + u_{yy} + αu_{x} & , x < 0 \\ u_{xx} − u_{y} + a(x, y)u & , x > 0 \end{matrix} \} .  (1)

in domain D = D_{0} ⋃ D_{1} ⋃ AB, where D_{0}(x < 0) is a characteristic triangular and D_{1}(x > 0) is a rectangular which adjoin to domain D_{0} by segment AB of the line x = 0. For indicated values of parameter α we found a representation of the general solution class R of system (1) in the domain D_{0}. For obtaining the representation of the solution we prove some important identities for hypergeometric functions. Using the solution of system (1) in domain do existency and uniqueness theorem for Gellerstedt problem is proved.