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Mathematics

The problem with periodicity conditions for the equations of mixed type with characteristic degeneracy

I. P. Egorova

Dept. of Higher Mathematics, Samara State Architectural and Building University, Samara, 443011, Russia

Abstract: For mixed type equation
$$ Lu\equiv u_{xx}+sgny\cdot |y|^m u_{yy}=0,\: 0<m<1\nonumber $$
\noindent in a rectangular domain $\{(x,y)|\quad 0<x<1,-\alpha<y<\beta\}$, where $m,\alpha,\beta$ – defined positive numbers, theorems of existence and uniqueness of the problem solvability with boundary solutions $u(0,y)=u(1,y)$, $u_x(0,y)=u_x(1,y)$, $-\alpha\leq y\leq \beta$; $u(x,\beta)=f(x)$, $u(x,-\alpha)=g(x),$ $0\le x\le 1$ are proved by the method of spectral analysis.

Keywords: eigenfunctions, spectral analysis.

UDC: 517.95

Received: 03.09.2009
Revised: 03.09.2009