Asymptotic solution of the one-dimensional wave equation with localized initial data and with degenerating velocity: I
Asymptotic solution of the one-dimensional wave equation with localized initial data and with degenerating velocity: I
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具有局部初始数据和简并速度的一维波动方程的渐近解：I
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
B. Tirozzi
中科院分区：
文献类型：
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作者：
S. Dobrokhotov;V. Nazaikinskii;B. Tirozzi
其中x是空间坐标，t是时间，D = D（x）是盆地深度（我们假设它是x的平滑函数），g是重力加速度。假设点x = 0对应于海岸线。更精确地说，对于x > 0，D（x）> 0，D（0）= 0，对于小x，D（x）= γx + O（x），其中γ = 0，并且等式(0.1)仅在域x > 0中被考虑。让我们提出下面的柯西问题，初始数据位于某个点x = a，a > 0的邻域中，对于方程：(0.1):
where x is the spatial coordinate, t is time, D = D(x) is the basin depth (which we assume to be a smooth function of x), and g is the acceleration due to gravity. Assume that the point x = 0 corresponds to the shoreline. More precisely, D(x) > 0 for x > 0, D(0) = 0, D(x) = γx + O(x) for small x, where γ = 0, and Eqs. (0.1) are regarded in the domain x > 0 only. Let us pose the following Cauchy problem with initial data localized in a neighborhood of some point x = a, a > 0, for Eq. (0.1):