论文标题
Boussinesq方程的扩展水波系统在有限的间隔：理论和数值分析
Extended water wave systems of Boussinesq equations on a finite interval: Theory and numerical analysis
论文作者
论文摘要
这里考虑的是NWOGU类型的一类BousSinesQ系统。这样的系统描述了非线性和分散水波的传播，例如孤立和海啸波。在理论上和数字上研究了该系统家族的有限间隔的初始有限值问题。首先，通过FOKA的统一变换来分析求解某个广义NWOGU系统的线性化。相应的分析揭示了两种类型的可接受边界条件，从而在有限的间隔内提出了非线性NWOGU系统的适当边界条件。然后，在弱和经典意义上，在一个正规化的Nwogu系统的情况下，建立了良好的性能，在初始边界值问题的背景下，描述了具有壁式条件的盆地中水波的动力学。此外，建议了一种新的修改后的盖尔金方法，以及时对该正则化系统的数值离散化，并证明其收敛及其最佳误差估计。最后，还提供了数字实验，说明了边界条件对垂直壁反射的影响。
Considered here is a class of Boussinesq systems of Nwogu type. Such systems describe propagation of nonlinear and dispersive water waves of significant interest such as solitary and tsunami waves. The initial-boundary value problem on a finite interval for this family of systems is studied both theoretically and numerically. First, the linearization of a certain generalized Nwogu system is solved analytically via the unified transform of Fokas. The corresponding analysis reveals two types of admissible boundary conditions, thereby suggesting appropriate boundary conditions for the nonlinear Nwogu system on a finite interval. Then, well-posedness is established, both in the weak and in the classical sense, for a regularized Nwogu system in the context of an initial-boundary value problem that describes the dynamics of water waves in a basin with wall-boundary conditions. In addition, a new modified Galerkin method is suggested for the numerical discretization of this regularized system in time, and its convergence is proved along with optimal error estimates. Finally, numerical experiments illustrating the effect of the boundary conditions on the reflection of solitary waves by a vertical wall are also provided.
