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Theorem. Let (y) be of the form (p(y)* or —(p(y) where (e.®) is real-valued and inf \(p(y) |>0 for a large yQ. Then the \y\^y0 _ " problem (1.1) has a unique solution u(x,y,t) in C°° (R+ X [0, T] ) for any (UQ (x, y) , u, (x, y) , f(x9 y,£), g (y, /) ) e C~ («i) X C" («i) X C~ (I : X [0, T\) XC°°(RX [0, T]) satisfying the compatibility condition of infinite order. Furthermore., the domain of dependence is finite.

Mixed problems in a quarter space for the wave equation with a singular oblique derivative