Electron. J. Diff. Eqns.,
Vol. 2007(2007), No. 100, pp. 122.
A numerical scheme using multishockpeakons to compute
solutions of the DegasperisProcesi equation
Håkon A. Hoel
Abstract:
We consider a numerical scheme for entropy weak solutions of the
DP (DegasperisProcesi) equation
. Multishockpeakons,
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 multishockpeakons relatively easy to simulate
numerically. We prove that if we are given a nonnegative initial
function
such that
is a positive Radon measure, then one can
construct a sequence of multishockpeakons which converges to
the unique entropy weak solution in
for any
.
From this convergence result, we construct a multishockpeakon 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.
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Håkon A. Hoel
Centre of Mathematics for Applications,
University of Oslo
P.O. Box 1053, Blindern, NO0316 Oslo, Norway
email: haakonah1@gmail.com
http://www.folk.uio.no/haakonah

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