A numerical scheme using multi-shockpeakons to compute solutions of the Degasperis-Procesi equation
| dc.contributor.author | Hoel, Hakon | |
| dc.date.accessioned | 2021-08-13T16:52:38Z | |
| dc.date.available | 2021-08-13T16:52:38Z | |
| dc.date.issued | 2007-07-19 | |
| dc.description.abstract | We consider a numerical scheme for entropy weak solutions of the DP (Degasperis-Procesi) equation ut - uₓₓt + 4uuₓ = 3uₓuₓₓ + uuₓₓₓ. Multi-shockpeakons, functions of the form u(x, t) = ∑ni=1 (mi(t) - sign(x - xi(t))ss(t))e-|x-xi(t)|, 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 u0 ∈ L1(ℝ) ∩ BV (ℝ) such that u0 - u0,x is a positive Radon measure, then one can construct a sequence of multi-shockpeakons which converges to the unique entropy weak solution in ℝ x [0, T) for any T > 0. From this convergence result, we construct a multi-shockpeakon based numerical scheme for solving the DP equation. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 22 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Hoel, H. A. (2007). A numerical scheme using multi-shockpeakons to compute solutions of the Degasperis-Procesi equation. <i>Electronic Journal of Differential Equations, 2007</i>(100), pp. 1-22. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/14316 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University-San Marcos, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2007, San Marcos, Texas: Texas State University-San Marcos and University of North Texas. | |
| dc.subject | Shallow water equation | |
| dc.subject | Numerical scheme | |
| dc.subject | Entropy weak solution | |
| dc.subject | Shockpeakon | |
| dc.subject | Shockpeakon collision | |
| dc.title | A numerical scheme using multi-shockpeakons to compute solutions of the Degasperis-Procesi equation | |
| dc.type | Article |