Hideo Deguchi
Abstract:
It is well-known that distributional solutions to the Cauchy
problem for
with
,
where H is the Heaviside function, are non-unique.
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: First-order hyperbolic equation;
discontinuous coefficient; generalized solutions.
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Hideo Deguchi Department of Mathematics, University of Toyama Toyama 930-8555, Japan email: hdegu@sci.u-toyama.ac.jp |
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