论文标题
通用0-霍尔姆 - 稳定方程的解决方案的存在，延续，持久性和动力学
Existence, continuation, persistence and dynamics of solutions for a generalized 0-Holm-Staley equation
论文作者
论文摘要
我们考虑了一个非本地演化方程式的家族，包括$ 0- $ HOLM-Staley方程。我们表明，只要最初的数据是不平凡的，就不会有所考虑的家庭就不会承受紧凑的解决方案。此外，我们证明了研究家庭解决方案的不同独特的延续结果。此外，研究了一些特殊解决方案，例如Pearmons和Kinks，并分析了它们的动态。还研究了解决方案的持久性能，并描述了$ 0- $ HOLM-Staley方程的全球解决方案的情况。特别是，全球解决方案的存在以及我们对解决方案的独特延续结果的演示部分回答了[A. A. Himonas和R. C. Thompson，通用Camassa-Holm方程的持久性和独特的延续，J。Math。物理学，第1卷55，论文091503，（2014）]。
We consider a family of non-local evolution equations including the $0-$Holm-Staley equation. We show that the family considered does not posses compactly supported solutions as long as the initial data is non-trivial. Also, we prove different unique continuation results for the solutions of the family studied. In addition, some special solutions, such as peakons and kinks, are studied and their dynamics are analyzed. Persistence properties of the solutions are also investigated as well as we describe the scenario for the global existence of solutions of the $0-$Holm-Staley equation. In particular, the prove of global existence of solutions as well as our demonstrations for unique continuation results of solutions partially answer some questions pointed out in [A. A. Himonas and R. C. Thompson, Persistence properties and unique continuation for a generalized Camassa-Holm equation, J. Math. Phys., vol. 55, paper 091503, (2014)].
