Lyne, O.D. and Williams, D. (2001) Weak Solutions for a Simple Hyperbolic System. Electronic Journal of Probability, 6 (20). pp. 1-21. ISSN 1083-6489.
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'.
|Uncontrolled keywords:||Weak solutions, Travelling Waves, Martingales, Branching Processes|
|Subjects:||Q Science > QA Mathematics (inc Computing science) > QA273 Probabilities|
|Divisions:||Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science|
|Depositing User:||Owen Lyne|
|Date Deposited:||02 Nov 2008 16:34|
|Last Modified:||05 Sep 2011 23:59|
|Resource URI:||http://kar.kent.ac.uk/id/eprint/7576 (The current URI for this page, for reference purposes)|
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