## On some boundary value problems for an ultrahyperbolic equation.(English)Zbl 0914.35073

In the space of variables $$x_1,x_2,y_1$$ and $$y_2$$ we consider the ultrahyperbolic equation $u_{y_1y_1}+ u_{y_2y_2}- u_{x_1x_1}-u_{x_2x_2} =F.\tag{1}$ Denote by $$D:-y_1<x_1<y_1$$, $$0<y_1<+\infty$$, a dihedral angle bounded by the characteristic surfaces $$S_1:x_1-y_1=0$$, $$0\leq y_1<+\infty$$, and $$S_2:x_1+y_1=0$$, $$0\leq y_1<+\infty$$, of equation (1). We shall consider a characteristic problem formulated as follows: in the domain $$D$$ find a solution $$u(x_1,x_2, y_1,y_2)$$ of equation (1) by the boundary conditions $$u|_{S_i}=f_i$$, $$i=1,2$$, where $$f_i$$, $$i=1,2$$, are given real functions on $$S_i$$ and $$(f_1-f_2)|_{S_1\cap S_2}=0$$.

### MSC:

 35L20 Initial-boundary value problems for second-order hyperbolic equations 35A05 General existence and uniqueness theorems (PDE) (MSC2000)
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