| 一类更广泛的Korteweg-de Vries方程的初边值问题 |
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| 引用本文： | 杨灵娥. 一类更广泛的Korteweg-de Vries方程的初边值问题[J]. 中南大学学报(自然科学版), 1988, 0(1) |
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| 作者姓名： | 杨灵娥 |
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| 作者单位： | 中南矿冶学院应用数学力学系 |
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| 摘 要： | 本文利用Galerkin方法和解的先验估计,研究了一类更广泛的Korteweg-de Vries方程的初边值问题。 u_t+f(u)_x-αu_(xx)+u_(xxx)=0 (x,t)∈R~+×[0,T] u(x,t)|_(t=0)=u_0(x) x∈R~+ u(x,t)|_(x=0)=0 u(x,t)→0 (x→∞)及 u_t+f(u)_x-u_(xxx)=0 u(x,t)|_(t=0)=u_0(x) x∈R~+ u(x,t)|_(x=0)=u_x(x,t)|x=0=0 u(x,t)→0,(x→∞)弱解的存在性,在适当的条件下,还可以得到古典解的存在性。
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| 关 键 词： | KdV方程 加辽金法 先验估计 边值问题 初值问题 广义解 存在性 |
THE INITIAL-BOUNDARY VALUE PROBLEM OF A GENERALIZED KdV EQUATION |
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| Yang Linge. THE INITIAL-BOUNDARY VALUE PROBLEM OF A GENERALIZED KdV EQUATION[J]. Journal of Central South University:Science and Technology, 1988, 0(1) |
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| Authors: | Yang Linge |
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| Affiliation: | Department of Applied Mathematics and Mechanics |
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| Abstract: | Using Galerkin Approximation and a prior estimate, we proved the existence of the weak solution for the initial-boundary value problem of a generalized KdV equation. Under the suitable conditions, we also proved the existence of a classical solution. |
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| Keywords: | KdV equation Galerkin's method a priori estimation boundary-value problem initial-value problem generalized solution existence |
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