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1.
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   

2.
研究了一类非线性强阻尼广义扰动发展方程问题.它们在数学、力学、物理学等领域中广泛出现.首先,引入一个行波变换,把相应的偏微分方程问题转化为行波方程问题并求出原典型问题的精确解.再用小参数方法和引入伸长变量构造了问题的渐近解.最后,用泛函分析的不动点理论证明了原非线性强阻尼广义扰动发展方程初值问题渐近行波解的存在性,并证明渐近解具有较高的精度和一致有效性.该文求得的渐近解是一个解析展开式,所以它还可继续进行解析运算,而单纯用数值模拟的方法是不行的.  相似文献   

3.
本文研究一类含小参数的Hill方程的初值问题,利用边值问题可解性条件及摄动理论中的伸缩参数法,给出寻求该初值问题近似周期解的方法,并以Mathieu方程为例作了具体计算.  相似文献   

4.
对于圆锥型和棱锥型Hamiltonian的Eikonal型方程,本文给出了一种几何方法,得出其初值问题解的表达式并且说明由此式给出的解为原初值问题的粘性解.首先用一个凸函数序列逼近Eikonal型方程中的Hamiltonian,再由Hopf-Lax公式给出方程序列的粘性解,最后证明了该粘性解序列会收敛到Eikonal方程的粘性解.  相似文献   

5.
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   

6.
舒级  张健 《数学进展》2007,36(4):453-458
本文讨论出现在吸引玻色-爱因斯坦凝聚中的一类带调和势的阻尼非线性Schr dinger方程.对照玻色-爱因斯坦凝聚的物理性质,证明了阻尼参数存在一个门槛值,即当阻尼参数大于该门槛值时,初值问题的解整体存在;当阻尼参数小于该门槛值时,其初值问题的解将在有限时间内坍塌.  相似文献   

7.
一类大气尘埃等离子体扩散模型研究   总被引:4,自引:3,他引:1  
研究了一类大气非线性尘埃等离子体扩散方程初值问题.首先在无扰动情形下,利用Fourier变换方法得到了尘埃等离子体扩散方程初值问题的精确解,接着引入一个同伦映射,并选取初始近似函数,再用同伦映射理论,依次求出非线性尘埃等离子体扰动初值问题的各次近似解析解.引用不动点理论,指出了近似解析解的有效性和各次近似解的近似度,用模拟曲线和表格给出近似对照例子.最后,简述了用同伦映射方法得到的近似解的物理意义.指出了用上述方法得到的各次近似解具有便于求解、精度高等优点.  相似文献   

8.
研究了在数学、力学中广泛出现的一类三阶非线性强阻尼发展扰动偏微分方程,并求其近似解析解.首先,构造一个泛函同伦映射,将方程的解表示以人工参数的幂级数形式,代入同伦映射,得到一个非线性扰动方程解的逐次迭代关系式,并考虑对应的一个无扰动项情形下的强阻尼发展方程,利用Fourier变换理论,求出其精确解.其次,以得到的精确解为同伦映射迭代式的初始函数,通过非线性扰动方程解的迭代关系式,再用Fourier变换法求解对应的方程.最后,便依次地得到了非线性强阻尼发展扰动偏微分方程的各次近似解析解.用上述方法得到的各次近似解,具有便于求解、精度高等特点.  相似文献   

9.
研究了Banach空间中非线性混合型微分-积分方程初值问题u′=f(t,u,Tu,Su),u(0)=x0的整体解,完全没有要求f的任何增性,利用Mnch不动点定理和比较结果得到了初值问题整体解的存在性和唯一解,并且给出了一致收敛于唯一解的迭代序列,改进推广和统一了已有的许多结果.  相似文献   

10.
一类非线性波动方程古典解的存在性   总被引:1,自引:0,他引:1  
研究了一类非线性波动方程的初边值问题,利用Faedo-Galerkin方法,证明了该初值问题古典解的存在性.  相似文献   

11.
Let (S, #, *) be an algebraic structure where # and * are binary operations with identities on the set S. Let (G, +) be an abelian group. We consider the functional equation (i) $$f(x * t, y)+ g(x, y\ \sharp\ t) = h(x, y)\ {\rm for\ all}\ x, y, t \in S,$$ where ?,g,h :S × S → G. As an application of (i) we solve $$f(x + t, y)- f(x, y) = -b(f(x, y+t)- f(x,y))\ {\rm for\ all}\ x, y, t \in S,$$ where ? :S × S → K (a field), and bK is a constant and b ≠ 0, ±1. If b = i, the pure imaginary unit, S = R and K = C, then the above equation may be considered as a discrete analogue of the Cauchy-Riemann equations. When (R, +, ?) is a commutative ring with 1, the functional equation (ii) $$\phi(y+xt)-\phi(xy+xt)=\phi(y+x)-\phi(xy+x)$$ for all x,y,t ∈ R, where ? : R → G, is basic to the general solutions of (i). We solve (ii) on certain rings and fields.  相似文献   

12.
The author proposes a two-dimensional generalization of Constantin-Lax-Majda model. Some results about singular solutions are given. This model might be the first step toward the singular solutions of the Euler equations. Along the same line (vorticity formulation), the author presents some further model equations. He possibly models various aspects of difficulties related with the singular solutions of the Euler and Navier-Stokes equations. Some discussions on the possible connection between turbulence and the singular solutions of the Navier-Stokes equations are made.  相似文献   

13.
In this paper, we consider extremely charged static perfect fluid distributions with a dilaton field in the framework of general relativity. By using calculus of variations, we establish the existence theorem for the solutions of this important gravitational system. We show that there is a continuous family of smooth solutions realizing asymptotically flat space metrics.  相似文献   

14.
We propose several approaches for solving two discrete-velocity Boltzmann equations using the rescaling ansatz and the truncated Painlevé expansions. We use solutions of the two- and three-dimensional Bateman equations for the singularity manifold conditions to reduce the problem to Riccati equations. Both equations fail the Painlevé test.  相似文献   

15.
Painlevé equations are studied on the basis of linear equations, which are generic for them. Different possible approaches are compared to each other. Formulas binding these approaches are derived. Symmetries demonstrated in the equations are also a subject of discussion.  相似文献   

16.
We prove global existence and uniqueness of solutions to theRarita-Schwinger evolution equations compatible with the constraints.We use a gauge fixing for the Rarita-Schwinger equations forhelicity 3/2 fields in curved space that leads to a straightforwardHilbert space framework for their study. We explain how theseresults might be applied to the global analysis of the fullEinstein vacuum equations and provide a complete analysis asa basis for such applications. These and a programme for developinga scattering/inverse scattering transform for the full Einsteinequations are discussed. 1991 Mathematics Subject Classification:83C60, 35Q75, 83C05, 35L45.  相似文献   

17.
变更Boussinesq方程和Kupershmidt方程的多孤子解   总被引:11,自引:1,他引:10  
使用王明亮引进的齐次平衡方法,求出了变更Boussinesq方程和Kupershmidt方程的多孤子解,而王明亮给出的变更的Boussinesq方程的单孤子解仅是上述结果的一种特殊情况。  相似文献   

18.
We describe a backward error analysis for stochastic differential equations with respect to weak convergence. Modified equations are provided for forward and backward Euler approximations to Itô SDEs with additive noise, and extensions to other types of equation and approximation are discussed.  相似文献   

19.
20.
This paper studies the fine structure of the Straubing hierarchy of star-free languages. Sequences of equations are defined and are shown to be sufficiently strong to characterize completely the monoid varieties of a natural subhierarchy of level one. In a few cases, it is also shown that those sequences of equations are equivalent to finite ones. Extensions to a natural sublevel of level two are discussed. This work was initiated while the author was at the Université de Montréal under an NSERC Postdoctoral Fellowship (Natural Sciences and Engineering Research Council of Canada). This work was supported by a grant from the Research Council of the University of North Carolina at Greensboro. Many thanks to the referee for his valuable comments and suggestions.  相似文献   

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