Localized solutions of one-dimensional non-linear shallow-water equations with velocity
Localized solutions of one-dimensional non-linear shallow-water equations with velocity
复制标题
一维非线性浅水速度方程的局部解
DOI：
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发表时间：
2010
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影响因子：
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通讯作者：
Brunello Tirozzi
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文献类型：
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作者：
Sergei Yu Dobrokhotov;Brunello Tirozzi
在无量纲变量中，非平底上的一维非线性浅水方程组D（x）= c（x），具有高程分量η（x，t）和速度v（x，t），由ηt + v [v（η + D）]/v（x）= 0，vt + vvx + ηx = 0给出。我们引入一个参数0 < μ π ι 1，并说函数f（y）局部化在点a > 0的μ-邻域中，如果f（a）= 1 + O（μ）且f（y）= O（μ），|y − a|> μ1−δ，δ > 0。当c（x）= x时，我们考虑Cauchy问题η| t=0 = η（x，μ），v| t=0 = v（x，μ），假设初始数据η，v都在x = a的邻域内.它的解用于描述长波浪冲击海岸[1]、[2]。下面的显着性质（在[1]中以另一种形式发现，也见[2]）的系统正在考虑可以建立直接微分。
In dimensionless variables, the one-dimensional non-linear system of shallow-water equations over a non-flat bottom D(x) = c(x) with elevation component η(x, t) and velocity v(x, t) is given by ηt + ∂[v(η + D)]/∂x = 0, vt + vvx + ηx = 0. We introduce a parameter 0 < μ ≪ 1 and say that a function f(y) is localized in the μ-neighbourhood of a point a > 0 if f(a) = 1 + O(μ) and f(y) = o(μ) for |y − a| > μ1−δ, δ > 0. In the case when c(x) = x, we consider the Cauchy problem η|t=0 = η(x, μ), v|t=0 = v(x, μ) for our system, assuming that the initial data η, v are localized in a neighbourhood of the point x = a. Its solution is used to describe long waves running onto a shore [1], [2]. The following remarkable property (discovered in another form in [1], see also [2]) of the system under consideration can be established by direct differentiation.