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# Weak Solutions for a Simple Hyperbolic System

Lyne, Owen D., Williams, David S. (2001) Weak Solutions for a Simple Hyperbolic System. Electronic Journal of Probability, 6 (20). pp. 1-21. ISSN 1083-6489. (KAR id:7576)

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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'.

Item Type: Article Weak solutions, Travelling Waves, Martingales, Branching Processes Q Science > QA Mathematics (inc Computing science) > QA273 Probabilities Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science Owen Lyne 02 Nov 2008 16:34 UTC 16 Feb 2021 12:19 UTC https://kar.kent.ac.uk/id/eprint/7576 (The current URI for this page, for reference purposes)
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