论文标题
一个半混凝土方案，该方案源自Camassa-Holm系统的全球保守解决方案的变异原理
A semi-discrete scheme derived from variational principles for global conservative solutions of a Camassa-Holm system
论文作者
论文摘要
我们定义了动力学和势能，以使拉格朗日力学的固定作用原理产生camassa-holm系统（2CH）作为管理方程。在离散这些能量之后，我们使用相同的变分原理来推导半污垢的方程系统作为2CH系统的近似值。离散式的仅在Lagrangian坐标中可用，需要倒置一个带有时变系数的liouville操作员。我们在初始时间显示了该操作员的基本解决方案，并具有适当的衰变。通过及时传播基本解决方案，我们定义了一个同等的半污染系统，我们证明存在独特的全球解决方案。最后，我们展示了如何使用半二淀粉系统的解决方案来构建一系列函数，融合了2CH系统的保守解决方案。
We define a kinetic and a potential energy such that the principle of stationary action from Lagrangian mechanics yields a Camassa--Holm system (2CH) as the governing equations. After discretizing these energies, we use the same variational principle to derive a semi-discrete system of equations as an approximation of the 2CH system. The discretizaton is only available in Lagrangian coordinates and requires the inversion of a discrete Sturm--Liouville operator with time-varying coefficients. We show the existence of fundamental solutions for this operator at initial time with appropriate decay. By propagating the fundamental solutions in time, we define an equivalent semi-discrete system for which we prove that there exists unique global solutions. Finally, we show how the solutions of the semi-discrete system can be used to construct a sequence of functions converging to the conservative solution of the 2CH system.
