Håkon A. Hoel
We consider a numerical scheme for entropy weak solutions of the DP (Degasperis-Procesi) equation . Multi-shockpeakons, functions of the form
are solutions of the DP equation with a special property; their evolution in time is described by a dynamical system of ODEs. This property makes multi-shockpeakons relatively easy to simulate numerically. We prove that if we are given a non-negative initial function such that is a positive Radon measure, then one can construct a sequence of multi-shockpeakons which converges to the unique entropy weak solution in for any . From this convergence result, we construct a multi-shockpeakon based numerical scheme for solving the DP equation.
Submitted June 13, 2007. Published July 19, 2007.
Math Subject Classifications: 35Q53, 37K10.
Key Words: Shallow water equation; numerical scheme; entropy weak solution; shockpeakon; shockpeakon collision.
Show me the PDF file (804 KB), TEX file, and other files for this article.
| Håkon A. Hoel |
Centre of Mathematics for Applications, University of Oslo
P.O. Box 1053, Blindern, NO-0316 Oslo, Norway
Return to the EJDE web page