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Weak Solutions for a Simple Hyperbolic System
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Owen D. Lyne, University of Nottingham
David Williams, University of Nottingham
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Abstract
The model studied concerns a simple first-order hyperbolic
system. The solutions in which one is most interested have
discontinuities which persist for all time, and therefore need to be
interpreted as weak solutions. We demonstrate existence and
uniqueness for such weak solutions, identifying a canonical `
exact' solution which is everywhere defined. The direct method
used is guided by the theory of measure-valued diffusions. The method
is more effective than the method of characteristics, and has the
advantage that it leads immediately to the McKean representation
without recourse to Itô's formula.
We then conduct computer studies of our model, both by integration
schemes (which do use characteristics) and by `random
simulation'.
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Full text: PDF
Pages: 1-21
Published on: August 15, 2001
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Electronic Journal of Probability. ISSN: 1083-6489 |
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