共查询到20条相似文献,搜索用时 250 毫秒
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提升钢线绳动态分析的分段线性化解法 总被引:1,自引:0,他引:1
梁兆正 《应用数学与计算数学学报》1996,10(2):35-43
本文在研究提升机绳系动态特性过程中,建立了一类非齐次边界条件混合问题的波动方程;应用离散化方法将非齐次项分段线性化,得到了该类波动方程的半解析解。 相似文献
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分数阶微积分是专门研究任意阶积分和微分的数学性质及其应用的领域,是传统的整数阶微积分的推广,分数阶微分方程是含有非整数阶导数的方程.时间分数阶扩散-波动方程可以用来模拟由传统的扩散-波动方程演变而来的反常扩散方程.考虑在有限区间上高维非齐次时间分数阶扩散-波动方程的初边值问题.利用分离变量法,导出了高维非齐次时间分数阶扩散-波动方程初边值问题的基本解. 相似文献
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四元数分析中的T算子与两类边值问题 总被引:12,自引:4,他引:12
本文研究四元数分析中的非齐次 Dirac方程.引入了这类方程的分布解即 T算子,证明了T算子的一些性质并考察了非齐次Dirac方程的Dirichlet边值问题,并将结果推广到高阶非齐次Dirac方程及这种方程的一类边值问题的情况. 相似文献
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结合对偶变量理论,为压电热弹性体混合层合板问题推导了齐次的控制方程和Hamilton等参元列式.首先根据广义的Hamilton变分原理推导了压电热弹性体非齐次的Hamilton正则方程.然后进一步考虑了热平衡方程与导热方程中变量的对偶关系,通过增加正则方程的维数,成功地将非齐次的正则方程转化为能独立求解压电热弹性体耦合问题的齐次控制方程.为了推导四节点Hamilton等参元列式的方便,可将温度梯度关系类比成本构关系并构建新的变分原理.齐次方程大大简化了人们在分析压电热弹性体耦合问题时,通常要求解非齐次方程和关于平衡方程和导热方程的二阶微分方程的繁琐方法,同时也减少了数值计算工作量. 相似文献
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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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Guangying Lv Mingxin Wang 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2013,64(4):1005-1023
This paper is concerned with traveling wave front and the stability as planar wave of reaction diffusion system on ${\mathbb{R}^{n}}$ , where n ≥ 2. Existence and asymptotic behavior of traveling wave front are discussed firstly. The stability as planar wave is established secondly by using super-sub solution method. Under initial perturbation that decays at space infinity, the perturbed solution converges to planar wave as ${t \rightarrow {\infty}}$ and the convergence is uniform in ${\mathbb{R}^{n}}$ . 相似文献
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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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Ví ctor H. Corté s Humberto Prado 《Proceedings of the American Mathematical Society》1997,125(4):1019-1026
This paper is concerned with the behavior in time for a certain class of dynamics which are discontinuous with respect to the time variable. We introduce the corresponding wave operators and we ensure their existence. Moreover, under suitable conditions this class of wave operators can be approximated in the strong sense by a sequence of ordinary wave operators. Our results can be applied to impulsive dynamical systems.
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V. M. Gordienko 《Siberian Mathematical Journal》2009,50(1):14-21
Some relation along an additional characteristic is constructed for a class of Friedrichs hyperbolic systems to which the wave equation is reduced. The statement is proven about preservation of a vortex. The conditions are stated for the solutions to Friedrichs hyperbolic systems of this class to remain solutions to the initial wave equation. 相似文献
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Siberian Mathematical Journal - We study the potential double wave equation and the system of spatial double wave equations. In the class of solutions of multiple wave type, these equations are... 相似文献
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J. G. Verwer 《Numerische Mathematik》2009,112(3):485-507
We study the numerical time integration of a class of viscous wave equations by means of Runge–Kutta methods. The viscous
wave equation is an extension of the standard second-order wave equation including advection–diffusion terms differentiated
in time. The viscous wave equation can be very stiff so that for time integration traditional explicit methods are no longer
efficient. A-Stable Runge–Kutta methods are then very good candidates for time integration, in particular diagonally implicit ones. Special
attention is paid to the question how the A-Stability property can be translated to this non-standard class of viscous wave equations.
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Nonlinear wave phenomena are of great importance in the nature, and have became for a long time a challenging research topic for both pure and applied mathematicians. In this paper the solitary wave, kink (anti-kink) wave and periodic wave solutions for a class of (3+1)-dimensional nonlinear equation were obtained by some effective methods from the dynamical systems theory. 相似文献
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A class of solitary wave solutions to a semi-linear wave equation on a pseudo-Riemannian manifold is studied. A construction of solutions which concentrate on geodesics is given. 相似文献