Numerical schemes for computing discontinuous solutions of the Degasperis–Procesi equation
Numerical schemes for computing discontinuous solutions of the Degasperis–Procesi equation
复制标题
DOI：
10.1093/imanum/drm003
复制
发表时间：
2007-03
影响因子：
2.1
通讯作者：
G. Coclite;K. Karlsen;N. Risebro
中科院分区：
文献类型：
--
作者：
G. Coclite;K. Karlsen;N. Risebro
最近的工作（COCLITE，G. M. & KARLSEN，K. H. 2006年，《论Degasperis-Procesi方程的适定性》（On the Well-posedness of the Degasperis-Procesi Equation）。J. Funct.分析：233，60-91）已经表明Degasperis-Procesi方程在（不连续）熵解类中是适定的。在本文中，我们构造了数值格式，并证明了它们收敛到熵解。此外，我们提供了几个数值例子强调，不连续（冲击）的解决方案的形式独立于初始数据的平滑度。我们专注于不连续的解决方案对比显着与现有的文献Degasperis-Procesi方程，这似乎强调与Camassa-Holm方程（双哈密顿结构，可积性，峰子解决方案和H 1作为相关的功能空间）的相似之处。
Recent work (COCLITE, G. M. & KARLSEN, K. H. (2006) On the well-posedness of the Degasperis-Procesi equation. J. Funct. Anal., 233, 60-91) has shown that the Degasperis-Procesi equation is well-posed in the class of (discontinuous) entropy solutions. In the present paper, we construct numerical schemes and prove that they converge to entropy solutions. Additionally, we provide several numerical examples accentuating that discontinuous (shock) solutions form independently of the smoothness of the initial data. Our focus on discontinuous solutions contrasts notably with the existing literature on the Degasperis-Procesi equation, which seems to emphasize similarities with the Camassa-Holm equation (bi-Hamiltonian structure, integrability, peakon solutions and H 1 as the relevant functional space).