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Weak Solutions for a Simple Hyperbolic System


 
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1. Title Title of document Weak Solutions for a Simple Hyperbolic System
 
2. Creator Author's name, affiliation, country Owen D. Lyne; University of Nottingham
 
2. Creator Author's name, affiliation, country David Williams; University of Nottingham
 
3. Subject Discipline(s) Mathematics
 
3. Subject Keyword(s) Weak solutions, Travelling waves, Martingales, Branching processses
 
3. Subject Subject classification 35L35; 60J27; 60G44
 
4. Description 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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7. Date (YYYY-MM-DD) 2001-08-15
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/93
 
10. Identifier Digital Object Identifier 10.1214/EJP.v6-93
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 6
 
12. Language English=en en
 
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