Electron. J. Diff. Equ.,
Vol. 2011 (2011), No. 76, pp. 125.
A linear firstorder hyperbolic equation
with discontinuous coefficient: distributional shadows
and propagation of singularities
Hideo Deguchi
Abstract:
It is wellknown that distributional solutions to the Cauchy
problem for
with
,
where H is the Heaviside function, are nonunique.
However, it has a unique generalized solution in the sense
of Colombeau. The relationship between its generalized solutions
and distributional solutions is established.
Moreover, the propagation of singularities is studied.
Submitted January 19, 2011. Published June 16, 2011.
Math Subject Classifications: 46F30, 35L03, 35A21.
Key Words: Firstorder hyperbolic equation;
discontinuous coefficient; generalized solutions.
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Hideo Deguchi
Department of Mathematics, University of Toyama
Toyama 9308555, Japan
email: hdegu@sci.utoyama.ac.jp

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