Lyne, Owen D. and Williams, David S. (2001) Weak Solutions for a Simple Hyperbolic System. Electronic Journal of Probability, 6 (20). pp. 121. ISSN 10836489. (Full text available)
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Abstract
The model studied concerns a simple firstorder 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 measurevalued 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 

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:  25 Jun 2014 13:09 
Resource URI:  https://kar.kent.ac.uk/id/eprint/7576 (The current URI for this page, for reference purposes) 
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