It is shown that, provided the nonlinearity is strictly convex, a discontinuity in the initial value of the solution of the equation
where and , is not immediately smoothed out even if the memory kernel is such that the solution of the problem where is a linear function is continuous for .
Submitted September 11, 2000. Published January 11, 2001.
Math Subject Classifications: 35L65, 35L67, 45K05.
Key Words: conservation law, discontinuous solution, memory.
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|Gustaf Gripenberg |
Institute of Mathematics
Helsinki University of Technology
P.O. Box 1100, FIN-02015 HUT, Finland
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