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
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