This article is cited in 1 paper

Differential Equations

The solution of Tricomi problem for the mixed type equation with Bessel operator with the method of the theory of the integral equations

R. M. Safina

Tatar State University of Humanities and Education

Abstract: In this article the existence and uniqueness of Tricomi problem solution is proven for Lavrentiev–Bizadze equation with the Bessel operator:
$$ x^{-k}\frac\partial{\partial x}\biggl(x^k\frac{\partial u}{\partial x}\biggr)+\operatorname{sign}y\frac{\partial^2u}{\partial y^2}=0 $$
in $D$ area limited with the rectifiable $\Gamma$ curve, $Oy$ axis and $OC\colon x+y=0$ and $BC\colon x-y=1$ characteristics, by method of the integral equations.

Keywords: the equation of mixed type, Tricomi problem, $B$-elliptic equation, $B$-hyperbolic equation, $N$ problem, Cauchy problem.

UDC: 517.956.6

MSC: 35M10, 35E15

Original article submitted 31/VII/2008
revision submitted – 18/X/2008

DOI: 10.14498/vsgtu604

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