A model containing both the Camassa–Holm and Degasperis–Procesi equations

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• 作者：Shaoyong Lai ; Yonghong Wu
• 关键词：Camassa– ; Holm equation ; Degasperis– ; Procesi ; Local well-posedness ; Weak solution
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2011
• 出版时间：15 February 2011
• 年：2011
• 卷：374
• 期：2
• 页码：458-469
• 全文大小：189 K

文摘

A nonlinear dispersive partial differential equation, which includes the famous Camassa–Holm and Degasperis–Procesi equations as special cases, is investigated. Although the H¹-norm of the solutions to the nonlinear model does not remain constants, the existence of its weak solutions in lower order Sobolev space H^s with is established under the assumptions u₀H^s and u_0xL^∞<∞. The local well-posedness of solutions for the equation in the Sobolev space H^s(R) with is also developed.