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1.
以分层理论为基础,讨论了不可压、无粘流体的Euler方程的形式可解性,并给出了各类不适定初值问题存在形式解的条件与计算方法。并讨论了超曲面上和超平面上初值问题的适定性并给出了存在不唯一解的例证。  相似文献   

2.
关于带未知函数线性附加项的简化Boussinesq方程   总被引:1,自引:0,他引:1  
应用分层理论研究带未知函数线性附加项的简化Boussinesq方程的稳定性, 以及使其初值问题适定的充要条件.最后给出初值问题不适定时具有若干形式解的实例.  相似文献   

3.
该文在L2中讨论了第一类算子方程Au=f当A-1无定义和A-1不是单值的情形下的不适定求解问题,给出了解存在的充要条件,当有解时,得到了形式解,多解时形式解就是最小范数解,并且得到了近似解表达式,给出了误差估计.  相似文献   

4.
Navier—Stokes方程稳定性研究(Ⅲ)   总被引:2,自引:1,他引:1  
施惟慧 《应用数学和力学》1994,15(12):1067-1073
本文给出Navier—Stokes方程某些初值问题存在C ̄2解的必要条件,并给出其在{t=0}上的初值问题不适定的例证。Navier—Stokes方程的初值问题是研究这个方程的基础问题之一。国内外很多学者在这方面的研究曾取得了不同程度的结果。法国时J.Leray教授就曾在某种意义下证明过Navier—Stokes方程某种初边值问题解的存在性 ̄[3].本文根据J.Hadamard的偏微分方程的基础理论 ̄[1].给出某些关键问题的严格定义,叙述一个有关Navipr-Stokes方程不稳定的基本定理。最后给出若干例证,其证明可参见[4]。  相似文献   

5.
讨论了一个具有Hysteresis的双曲方程,并给出这个方程一维初值问题古典解和多维初边值问题强解的存在唯一性.  相似文献   

6.
无粘、可压、绝热流体的Euler方程初值问题的适定性   总被引:1,自引:1,他引:0  
根据分层理论提供的基本方法,讨论Euler方程的初值问题的适定性,给出了方程的典型初边值问题适定性的判别条件,确定了Euler方程的局部(准确)解的解空间构造,对适定问题给出了解析解的计算公式·  相似文献   

7.
给出了R3×R上的Navier_Stokes方程初值问题存在形式解的充要条件 ,同时给出了一个计算实例·  相似文献   

8.
研究了一类非线性演化方程初值问题.通过不变子空间方法,这类初值问题被约化为常微分方程组的初值问题.这类初值问题是适定的.本文给出了这类初值问题关于时间变量t的幂级数解.  相似文献   

9.
本文用Kato关于拟线性演化方程的初值问题的存在性定理证明了浅水波方程在半无界直线上初值问题局部解的存在性。用解的先估计证明了整体解的存在性或解的Blow-up性质,并给出了解关于x的渐近估计。  相似文献   

10.
非线性扰动Klein-Gordon方程初值问题的渐近理论   总被引:1,自引:0,他引:1  
在二维空间中研究一类非线性扰动Klein_Gordon方程初值问题解的渐近理论.首先利用压缩映象原理,结合一些先验估计式及Bessel函数的收敛性,根据Klein_Gordon方程初值问题的等价积分方程,在二次连续可微空间中得到了初值问题解的适定性;其次,利用扰动方法构造了初值问题的形式近似解,并得到了该形式近似解的渐近合理性;最后给出了所得渐近理论的一个应用,用渐近近似定理分析了一个具体的非线性Klein_Gordon方程初值问题解的渐近近似程度·  相似文献   

11.
比较了Navier-Stokes方程和Euler方程的稳定性;并以它们的典型初值问题为例,分析了Navier-Stokes方程和Euler方程稳定性不同的原因.  相似文献   

12.
We obtain new gauge-invariant forms of two-dimensional integrable systems of nonlinear equations: the Sawada-Kotera and Kaup-Kuperschmidt system, the generalized system of dispersive long waves, and the Nizhnik-Veselov-Novikov system. We show how these forms imply both new and well-known twodimensional integrable nonlinear equations: the Sawada-Kotera equation, Kaup-Kuperschmidt equation, dispersive long-wave system, Nizhnik-Veselov-Novikov equation, and modified Nizhnik-Veselov-Novikov equation. We consider Miura-type transformations between nonlinear equations in different gauges. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 160, No. 1, pp. 35–48, July, 2009.  相似文献   

13.
Bethuel et al.  and  and Chiron and Rousset [3] gave very nice proofs of the fact that slow modulations in time and space of periodic wave trains of the NLS equation can approximately be described via solutions of the KdV equation associated with the wave train. Here we give a much shorter proof of a slightly weaker result avoiding the very detailed and fine analysis of ,  and . Our error estimates are based on a suitable choice of polar coordinates, a Cauchy–Kowalevskaya-like method, and energy estimates.  相似文献   

14.
15.
We obtain exact solutions U(x, y, z, t) of the three-dimensional sine-Gordon equation in a form that Lamb previously proposed for integrating the two-dimensional sine-Gordon equation. The three-dimensional solutions depend on arbitrary functions F(α) and ϕ(α,β), whose arguments are some functions α(x, y, z, t) and β(x, y, z, t). The ansatzes must satisfy certain equations. These are an algebraic system of equations in the case of one ansatz. In the case of two ansatzes, the system of algebraic equations is supplemented by first-order ordinary differential equations. The resulting solutions U(x, y, z, t) have an important property, namely, the superposition principle holds for the function tan(U/4). The suggested approach can be used to solve the generalized sine-Gordon equation, which, in contrast to the classical equation, additionally involves first-order partial derivatives with respect to the variables x, y, z, and t, and also to integrate the sinh-Gordon equation. This approach admits a natural generalization to the case of integration of the abovementioned types of equations in a space with any number of dimensions. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 158, No. 3, pp. 370–377, March, 2009.  相似文献   

16.
We obtain the super stability of Cauchy's gamma-beta functional equation
B(x,y)f(x+y)=f(x)f(y),  相似文献   

17.
18.
In this paper we give exact solutions for a forced Burgers equation. We make use of the generalized Cole-Hopf transformation and the traveling wave method.  相似文献   

19.
Discretisation of the integral equations of acoustic scattering yields a system of linear equations with full coefficient matrices. In recent years a number of fast algorithms for the solution of this system have been proposed. In this paper we present a complete analysis for a fast multipole method for the Helmholtz equation. A one-level diagonal form of the multipole method is applied to a hypersingular integral equation arising from 2d scattering theory. The error of the approximation is analysed and the results used to establish the complexity of the method.  相似文献   

20.
We search for traveling-wave solutions of the class of PDEswhere Ap(Q),Br(Q),Cs(Q),Du(Q) and F(Q) are polynomials of Q. The basis of the investigation is a modification of the method of simplest equation. The equations of Bernoulli, Riccati and the extended tanh-function equation are used as simplest equations. The obtained general results are illustrated by obtaining exact solutions of versions of the generalized Kuramoto-Sivashinsky equation, reaction-diffusion equation with density-dependent diffusion, and the reaction-telegraph equation.  相似文献   

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