ACTA issues

On connection among values of solutions of the Tricomi problem on the sides of characteristic triangles

A. Maher, N. B. Pleshchinskii

Acta Sci. Math. (Szeged) 74:1-2(2008), 121-133

Abstract. This paper deals with the Tricomi problem for the Lavrent'ev-Bitsadze equation for the special case in which the elliptic part of the domain is a semi-disk. The connections amongst values of solutions of the Tricomi problem for the Lavrent'ev--Bitsadze equation on the characteristics in the hyperbolic part of the mixed domain are investigated. Inversion formulas for some integral operators are obtained. It is shown that Gellerstedt problems can be reduced to the Tricomi problem. Henceforth, two theorems and one corollary are obtained for the problem under consideration.

AMS Subject Classification (1991): 35M

Keyword(s): the Tricomi problem, the Lavrent'ev-Bitsadze equation, the Gellerstedt problems

Received April 4, 2007, and in revised form October 24, 2007. (Registered under 6007/2009.)