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1.
本文研究一个描述离子在向列型液晶中输运和扩散的非线性偏微分方程模型.该模型耦合了对应于电势满足Maxwell’s方程的离子的连续性方程的Nernst-Planck系统,控制液晶流演变的不可压Naiver-Stokes方程与关于液晶方向场的非线性Allen-Cahn型方程.我们利用能量方法证明了该系统的大初值经典解的局部存在性和小初值经典解的整体存在性.  相似文献   

2.
闵涛  任菊成  耿蓓 《数学杂志》2014,34(4):766-772
本文主要研究了一类非线性Klein-Gordon方程.利用Fourier谱方法对一类非线性Klein-Gordon方程的求解,给出了求解的离散过程,并通过了数值模拟与文献结果进行了对比.结果表明这种方法对于求解此类非线性Klein-Gordon方程具有很好的效果.  相似文献   

3.
非线性抛物型方程初边值问题解的Blow up性质   总被引:1,自引:0,他引:1  
本文研究一类非线性抛物型方程具有非线性边界条件的初边值问题.利用抛物型方程最大值原理和凸性方法证明了该问题的解在有限时间内爆破.推广了文献[7-9]的结果.  相似文献   

4.
具有积分型非线性schrodinger方程是在研究非线性Langmuir波时考虑到离子惯性作用而导出的.本文讨论了二维空间中具有积分型非线性schrodinger方程组的初值问题,用积分估计方法证明了整体解的存在唯一性.  相似文献   

5.
丛文相 《应用数学》1995,8(4):389-395
本文针对地震勘探中提出一类重要的2-D波动方程反演问题,通过定义一个新的非线性算子将2-D波动方程的反演问题归结为一个新的非线性算子方程,详细讨论了非线性算子的性质,给出了求解反问题的迭代方法,并证明了这种迭代方法的收敛性。  相似文献   

6.
使用Arnold等人提出的求解椭圆方程的间断有限元的一般框架及新的处理非线性对流项的方法,得到了非线性对流扩散方程的三层隐-显hp-LDG方法的误差估计.对Burgers方程进行了数值计算,计算结果验证了文中得到的理论结果.  相似文献   

7.
非线性粘弹性柱的稳定性和混沌运动   总被引:18,自引:2,他引:16  
研究了受轴向周期力作用的各向同性简支柱的动力学稳定性· 假定粘弹性材料满足Lea derman非线性本构关系· 导出运动方程为非线性偏微分_积分方程 ,并利用Galerkin方法简化为非线性微分_积分方程· 应用平均法进行了稳定性分析 ,并用数值结果进行验证· 数值结果还表明系统可能存在混沌运动·  相似文献   

8.
非线性非完整系统Vacco动力学方程的积分方法   总被引:3,自引:0,他引:3  
本文给出积分非线性非完整系统Vacco动力学方程的积分方法。首先,将Vacco动力学方程表示为正则形式和场方程形式:然后,分别用梯度法,单分量法和场方法积分相应完整系统的动力学方程,并加上非完整约束对初条件的限制而得到非线性非完整系统Vacco动力学方程的解.  相似文献   

9.
本文讨论了定常K-S方程关于伽辽金方法和非线性伽辽金方法的收敛性和最大模估计;对相同模数而言,两者的误差阶完全一致,数值结果表明非线性伽辽金方法同样成功地计算出了K-S方程的分歧解,并且在计算时间方面非线性伽辽金方法比伽辽金方法要少得多。  相似文献   

10.
本文研究一般非线性渗流方程解的一种性态.利用De Giorgi方法与BCP估计相结合,得到了一般非线性渗流方程正性的扩展性质,推广了非线性渗流方程的结果.  相似文献   

11.
HybridFiniteElementMethodforTwo┐phaseMiscibleDisplacementinPorousMedia*)LiangDong(梁栋)ChengAijie(程爱杰)(DepartmentofMathematics,...  相似文献   

12.
微分连续正则化方法与一维声波方程系数反演问题求解   总被引:4,自引:0,他引:4  
本文将求解非线性方程组的微分连续法与求解不问题的Tikhonov正则化方法结合起来,形成了兼有大范围收性与稳定性的“微分连续正则化方法”,给出了方法的收敛性分析,文中最后给出的关于一维波动方程反问题的计算实例表明了方法的有效性。  相似文献   

13.
本文利用文[1]中的Gauss-Seidel迭代方法来研究非线性时变离散系统的渐近稳定性,得到了渐近稳定性的若干代数判据,为离散系统稳定性的研究提供了一种新的方法。  相似文献   

14.
本文将摄动法和有限条法结合起来进行矩形板的大挠度弯曲分析.用摄动的概念,将非线性微分方程组化为一系列线性微分方程组,然后用有限条法解这些线性微分方程组.  相似文献   

15.
The performance of automatic codes for solving reaction–diffusion systems is controlled by a variety of parameters. Some of them are invisible to the user while others can be modified. For the latter default values are available. The effects of four such parameters are studied for a code that couples the method-of-lines in time with a high-order h-refinement finite element strategy in space. The key parameters considered are the ratio of the temporal error tolerance to the spatial error tolerance, two parameters governing convergence of the iterative methods for the linear and nonlinear systems, and the number of time steps between regridding. These parameters are typical in method-of-lines based codes. Computations on a model problem demonstrate that both small and large temporal to spatial error ratios lead to performance degradation as does less frequent regridding. They also show that insufficient convergence in the nonlinear solver can reduce the reliability of the spatial error estimates.  相似文献   

16.
This paper applies He’s Energy balance method (EBM) to study periodic solutions of strongly nonlinear systems such as nonlinear vibrations and oscillations. The method is applied to two nonlinear differential equations. Some examples are given to illustrate the effectiveness and convenience of the method. The results are compared with the exact solution and the comparison showed a proper accuracy of this method. The method can be easily extended to other nonlinear systems and can therefore be found widely applicable in engineering and other science.  相似文献   

17.
In this paper, a novel method called variational iteration method is proposed to solve nonlinear partial differential equations without linearization or small perturbations. In this method, a correction functional is constructed by a general Lagrange multiplier, which can be identified via variational theory. An analytical solution can be obtained from its trial-function with possible unknown constants, which can be identified by imposing the boundary conditions, by successively iteration.  相似文献   

18.
一类非线性波动方程的显式精确解   总被引:14,自引:0,他引:14  
本文用直接方法和假设的一种结合求出了一类较广泛的非线性波动方程utt-a1uxx+a2ut+a3u+a4uS^2+a5u^3=0的一些显式精确行波解,贱个有重要的非线性数学物理方程,如φ^4方程,Klein-Gordon方程,Sine-Gordon方程,及Sinh-Gordon方程的近似,Landau-Ginzburg-Higgs方程,Duffing方程,非线性电报方程等都可作为该方程的特殊情形得  相似文献   

19.
In this work, we implement a relatively new analytical technique, the exp-function method, for solving nonlinear special form of generalized nonlinear (2 + 1) dimensional Broer-Kaup-Kupershmidt equation, which may contain high nonlinear terms. This method can be used as an alternative to obtain analytic and approximate solutions of different types of fractional differential equations which applied in engineering mathematics. Some numerical examples are presented to illustrate the efficiency and reliability of exp method. It is predicted that exp-function method can be found widely applicable in engineering.  相似文献   

20.
In this work, we implement a relatively new analytical technique, Exp-Function method, for solving special form of generalized nonlinear Radhakrishnan, Kundu and Laskshmanan equation (RKL), which may contain highly nonlinear terms. This method can be used as an alternative to obtain analytic and approximate solutions of different types of differential equations applied in engineering mathematics. Some numerical examples are presented to illustrate the efficiency and reliability of Exp-Function method. It is predicted that Exp-Function method can be found widely applicable in engineering problems.  相似文献   

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