论文标题
两种卷积型单向波方程的溶液的比较
A Comparison of Solutions of Two Convolution-Type Unidirectional Wave Equations
论文作者
论文摘要
在这项工作中，我们证明了一类非线性分散单向波方程的比较结果。一维波的色散性质是由于空间中的卷积积分而发生的。对于内核函数的两个特定选择，本杰明·巴诺 - 摩尼方程和rosenau方程分别特别适合于模拟水波和弹性波，是该类别的两个成员。我们首先证明了非局部单向波方程的凯奇问题的能量估计。然后，对于相同的初始数据，我们考虑了两个不同的解决方案，与两个不同的内核函数相对应。我们的主要结果是，如果两个内核函数在长波限制中具有相似的分散特性，则解决方案之间的差异仍然很小。作为此比较结果的样本案例，我们提供了双曲线保护定律的近似值。
In this work, we prove a comparison result for a general class of nonlinear dispersive unidirectional wave equations. The dispersive nature of one-dimensional waves occurs because of a convolution integral in space. For two specific choices of the kernel function, the Benjamin-Bona-Mahony equation and the Rosenau equation that are particularly suitable to model water waves and elastic waves, respectively, are two members of the class. We first prove an energy estimate for the Cauchy problem of the nonlocal unidirectional wave equation. Then, for the same initial data, we consider two distinct solutions corresponding to two different kernel functions. Our main result is that the difference between the solutions remains small in a suitable Sobolev norm if the two kernel functions have similar dispersive characteristics in the long-wave limit. As a sample case of this comparison result, we provide the approximations to the hyperbolic conservation law.
