Open AccessMixed Problems In a Quarter Space for the Wave Equation with a Singular Oblique Derivative
Author(s) -
Hideo Soga
Publication year - 1979
Publication title -
publications of the research institute for mathematical sciences
Language(s) - English
Resource type - Journals
eISSN - 1663-4926
pISSN - 0034-5318
DOI - 10.2977/prims/1195187869
Subject(s) - mathematics , oblique case , domain (mathematical analysis) , order (exchange) , combinatorics , wave equation , space (punctuation) , compatibility (geochemistry) , mathematical analysis , mathematical physics , economics , linguistics , geochemistry , finance , geology , philosophy
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.
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