Abstract
(a) The method of spherical means The wave equation for a function u(x1,...,x n ,t)= u(x,t) of n space variables x1,...,x n and the time t is given by
with a positive constant c. The operator “□” defined by (1.1) is known as the D’Alembertian. For n=3 the equation can represent waves in acoustics or optics, for n=2 waves on the surface of water, for n=1 sound waves in pipes or vibrations of strings. In the initial-value problem we ask for a solution of (1.1) defined in the (n+1)-dimensional half space t>0 for which
([15], [19])
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© 1978 Springer-Verlag New York Inc.
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John, F. (1978). Hyperbolic equations in higher dimensions. In: Partial Differential Equations. Applied Mathematical Sciences, vol 1. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-0059-5_5
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DOI: https://doi.org/10.1007/978-1-4684-0059-5_5
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