共查询到20条相似文献,搜索用时 15 毫秒
1.
XiaoFengLIU YongYangJIN 《数学学报(英文版)》2005,21(2):393-408
We consider the Cauchy problem of a shallow water equation and its local wellposedness. 相似文献
2.
建立了弱耗散非线性浅水波方程的局部适定性,对于不同的初始值,我们分别得到了解的整体存在性和解的爆破。 相似文献
3.
Zhao Hui HUO Bo Ling GUO 《数学学报(英文版)》2005,21(5):1191-1196
The Cauchy problem of the generalized Korteweg-de Vries-Benjamin-Ono equation is considered, and low regularity and limit behavior of the solutions are obtained. For k = 1, local well- posedness is obtained for data in H^s(R)(s 〉 -3/4). For k = 2, local result for data in H^S(R)(s 〉1/4) is obtained. For k = 3, local result for data in H^S(R)(s 〉 -1/6) is obtained. Moreover, the solutions of generalized Korteweg-de Vries-Benjamin-Ono equation converge to the solutions of KdV equation if the term of Benjamin-Ono equation tends to zero. 相似文献
4.
Some properties of the singular integral operator G(⋅) and the solvability of Cauchy problem for the singular integral-differential equations (1.1) and (1.2) of finite-depth fluids are studied. 相似文献
5.
The local well-posedness of the Cauchy problem for the coupled Hirota equations is established in Sobolev spaces Hs×Hs by the Fourier restriction norm method. 相似文献
6.
We study periodic boundary problem and Cauchy problem for the fluid dynamic equation in geophysics. The generalized and classical global solution of the mentioned problems are established. The method employed in this paper is Galerkin approximation and integral estimates. 相似文献
7.
Yueling Jia 《偏微分方程(英文版)》2003,16(3):275-288
The Cauchy problem for the generalized Korteweg-de Vries-Burgers equation is considered and the local existence and uniqueness of solutions in L^q(0, T;L^p) ∩ L^∞(0, T; \dot{H}^{-s})(0 ≤ s < 1) are obtained for initial data in \dot{H}^{-s}. Moreover, the local solutions are global if the initial data are sufficiently small in critical case. Particularly, for s = 0, the generalized Korteweg-de Vries-Burgers equation satisfies the energy equality, so the initial data can be arbitrarily large to obtain the global solution. 相似文献
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Yunyun Ma & Fuming Ma 《数学研究通讯:英文版》2012,28(4):300-312
In this paper, we consider the reconstruction of the wave field in a
bounded domain. By choosing a special family of functions, the Cauchy problem
can be transformed into a Fourier moment problem. This problem is ill-posed. We
propose a regularization method for obtaining an approximate solution to the wave
field on the unspecified boundary. We also give the convergence analysis and error
estimate of the numerical algorithm. Finally, we present some numerical examples to
show the effectiveness of this method. 相似文献
10.
§1. IntroductionAbouttwentyyears,thesolutionsintegralrepresentationsofimhomogeneousCauch-Rie-mannequationsandsup-normestimateshavebeengivenbyHenkin[4]andGrauert-Lieb[5]from1970,usherinanewtimes,developinginseveralcomplexvariables,abouttwentyyearsafter70s,integralrepresentationmethodshadbeenappliedextensivelyandfolurishing.AttheverybeginingofresearchinChina,oneoftheoutstandingpioneersisprofessorZhongTongdehasgivenabrilliantandexpoundprofoundly,comprehensiondevelopingandsumming-upinhismonog… 相似文献
11.
许晓革 《数学的实践与认识》2005,35(5):225-228
均衡作用法给出了一种求非线性发展方程孤波解的有效方法.利用该方法,运用计算机符号计算,求出了变系数的一般浅水波方程的孤子解. 相似文献
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采用了一种新的方法来求解浅水波方程和Klein-Gordon的行波解.在该方法下,Klein-Gordon方程和浅水波方程都得到了其精确的周期孤立波解,从而该方法的有效性得到了验证. 相似文献
14.
This paper is concerned with the Cauchy problem for the modified Helmholtz equation in an infinite strip domain 0 < x≤ 1, y ∈ R. The Cauchy data at x = 0 is given and the solution is then sought for the interval 0 < x ≤1. This problem is highly ill-posed and the solution (if it exists) does not depend continuously on the given data. In this paper, we propose a fourth-order modified method to solve the Cauchy problem. Convergence estimates are presented under the suitable choices of regularization parameters and the a priori assumption on the bounds of the exact solution. Numerical implementation is considered and the numerical examples show that our proposed method is effective and stable. 相似文献
15.
This paper concerns with the Cauchy problem for the nonlinear double dispersive wave equation.By the priori estimates and the method in [9],It proves that the Cauchy problem admits a unique global classical solution.And by the concave method,we give sufficient conditions on the blowup of the global solution for the Cauchy problem. 相似文献
16.
陈涌 《数学年刊A辑(中文版)》2016,37(2):211-226
研究了在H~1(R)中带阻尼的随机浅水波方程的随机吸引子的存在性.主要工具是Fourier限制范数方法以及将解分解为衰减部分与正则部分. 相似文献
17.
给出一种化归方法,通过适当的手段巧妙地将求解波动方程初值问题化归为传输方程的初值问题或热传导方程的初值问题. 相似文献
18.
关于一类空间齐次推广的耗散碰撞Boltzmann方程Cauchy问题 ,对于一般的初始条件得到了正古典解的存在唯一性 . 相似文献
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Wengu Chen 《偏微分方程通讯》2013,38(10):1739-1762
This note shows the existence of a sharp bilinear estimate for the Bourgain-type space and gives its application to the optimal local well/ill-posedness of the Cauchy problem for the Benjamin equation. 相似文献