共查询到20条相似文献,搜索用时 15 毫秒
1.
Burgers-KdV方程的二类行波解 总被引:5,自引:0,他引:5
在熊树林关于“Burgers-KdV方程的一类解析解”工作的基础上,给出了Burgers-KdV方程的另外两类精确行波解,扩充了范恩贵等人工作的结果. 相似文献
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The authors show the existence and uniqueness of solution for a class of stochastic wave equations with memory. The decay estimate of the energy function of the solution is obtained as well. 相似文献
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本文研究了两个空间变量的拟线性退缩抛物方程Cauchy问题广义解的正则性问题。推广了文献[1]的结果。 相似文献
4.
This article investigates backward stochastic Volterra integral equations in Hilbert spaces. The existence and uniqueness of their adapted solutions is reviewed. We establish the regularity of the adapted solutions to such equations by means of Malliavin calculus. For an application, we study an optimal control problem for a stochastic Volterra integral equation driven by a Hilbert space-valued fractional Brownian motion. A Pontryagin-type maximum principle is formulated for the problem and an example is presented. 相似文献
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本文给出了磁微极流体方程弱解的一个新的正则性准则:如果u满足uz ∈Lq(0,T;Lp(R3)),其中p≥3且满足3/p+2/q≤1,那么弱解(u,ω,b)在(0,T)是光滑解. 相似文献
6.
结合子方程和动力系统分析的方法研究了一类五阶非线性波方程的精确行波解.得到了这类方程所蕴含的子方程, 并利用子方程在不同参数条件下的精确解, 给出了研究这类高阶非线性波方程行波解的方法, 并以Sawada Kotera方程为例, 给出了该方程的两组精确谷状孤波解和两组光滑周期波解.该研究方法适用于形如对应行波系统可以约化为只含有偶数阶导数、一阶导数平方和未知函数的多项式形式的高阶非线性波方程行波解的研究. 相似文献
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The exact explicit traveling solutions to the two completely integrable sixthorder nonlinear equations KdV6 are given by using the method of dynamical systems and Cosgrove's work.It is proved that thes... 相似文献
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In two-space-dimensional case we get the sharp lower bound of the life-span of classical solutions to the Cauchy problem with small initial data for fully nonlinear wave equations of the form ◻u = F (u, Du, D_zDu) in which F(\hat{λ}) = O(|\hat{λ}|^{1+α}) with α = 2 in a neighbourhood of \hat{λ} = 0. The cases α = 1 and α ≥ 3 have been considered respectively in [1] and [2]. 相似文献
9.
Pao-Liu Chow 《随机分析与应用》2013,31(3):543-551
This article is concerned with explosive solutions of the initial-boundary problem for a class of nonlinear stochastic wave equations in a domain 𝒟 ? ? d . Under appropriate conditions on the initial data, the nonlinear term and the noise intensity, it is proved in Theorem 3.4 that there cannot exist a global solution and the local solution will blow up at a finite time in the mean L p ? norm for p ≥ 1. An example is given to show the application of this theorem. 相似文献
10.
Changxing Miao 《偏微分方程(英文版)》2003,16(1):75-81
In this note we shall give a simple proof of a result in [1] which gives a sufficient condition for the regularity of solutions to the Navier-Stokes equation in R^n based on estimates on the vorticity. 相似文献
11.
利用Darboux和一个可化为标准Bernoulli方程的4阶常微分方程,统一地处理了三个著名方程KdV方程,Kadomtsev-Petviashvili(KP)方程和Hirota-Satsuma(HS)方程的求解问题.给出了这些方程一批新的具有更为丰富形式的精确解,其中包括孤波解和行波解. 相似文献
12.
基于计算机代数系统,研究了一类Benney-Kawahara-Lin方程,利用行波变换法给出了它的一类孤波解,并分析了所得解的物理意义. 相似文献
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YeMinCHEN 《数学学报(英文版)》2004,20(6):1103-1118
The aim of this paper is to study the regularity of solutions to the Dirichlet problems for general second-order elliptic equations in Lebesgue and Morrey spaces. We consider both nondivergence and divergence forms and the coefficients of principle terms are assumed to be in VMO. 相似文献
17.
Let M be a compact Riemannian manifold. We prove existence of a global weak solution of the stochastic wave equation D t u t = D x u x + (X u + λ0(u)u t + λ1(u)u x )[Wdot] where X is a continuous vector field on M, λ0 and λ1 are continuous vector bundles homomorphisms from TM to TM, and W is a spatially homogeneous Wiener process on ? with finite spectral measure. We use recently introduced general method of constructing weak solutions of SPDEs that does not rely on any martingale representation theorem. 相似文献
18.
Qin Tiehu 《偏微分方程(英文版)》1990,3(1)
Applying Nash-Moser's implicit function theorem, the author proves the existence of periodic solution to nonlinear wave equation u_{tt} - u_{xx} + εg(t, x, u, u_t, u_x, u_{tt}, u_{tx}, u_{xx}) = 0 with a dissipative boundary condition, provided ε is sufficiently small. 相似文献
19.
本文在系数为非Lipschitz条件下(Lipschitz和线性增长作为其特例),通过构造逐次逼近列的方法证明了随机波动方程适度解的存在唯一性. 相似文献