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31.
An implicit quasi-monotone second-order accurate method is proposed for analyzing the spiral Couette flow of a rarefied gas between coaxial cylinders. The basic advantages of the method over the conventional method of stationry iterations are that the former is conservative with respect to the collision integral, has a simple software implementation for any types of boundary conditions, and applies to a wide range of Knudsen numbers. 相似文献
32.
Zhao Hanzhong 《Acta Mechanica Solida Sinica》2002,15(2):156-162
A finite difference/boundary integral procedure to determine the acoustic reflected pressure from a fluid-loaded bi-laminated
plate is described. The bi-laminate is composed of a piezoelectric layer and an elastic layer in contact with the fluid, and
is held by an acoustically hard baffle. In the numerical model, the fluid pressure at fluid/solid interface is replaced by
a continuum of point sources weighted by the normal acceleration of the elastic plate, and the governing equation system is
solved in the solid domain. With the normal acceleration found, the reflected pressure in the fluid is determined by an integral
expression involving the Green's function. It is demonstrated that an appropriate applied voltage potential across the piezoelectric
layer has the effect of cancelling either the reflected or scattered pressure of the plate at any chosen field points in the
fluid.
Project supported by the National Natural Science Foundation of China (No. 10172039). 相似文献
33.
Mehdi Dehghan 《Numerical Methods for Partial Differential Equations》2002,18(2):193-202
Developement of numerical methods for obtaining approximate solutions to the three dimensional diffusion equation with an integral condition will be carried out. The numerical techniques discussed are based on the fully explicit (1,7) finite difference technique and the fully implicit (7,1) finite difference method and the (7,7) Crank‐Nicolson type finite difference formula. The new developed methods are tested on a problem. Truncation error analysis and numerical examples are used to illustrate the accuracy of the new algorithms. The results of numerical testing show that the numerical methods based on the finite difference techniques discussed in the present article produce good results. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 193–202, 2002; DOI 10.1002/num.1040 相似文献
34.
Soliton interaction under the influence of higher-order effects 总被引:6,自引:0,他引:6
In this paper, we present exact N-soliton solution by employing simple, straightforward Darboux transformation based on the Lax pair for Hirota equation, a higher-order nonlinear Schrödinger (HNLS) equation. As examples, one- and two-soliton solutions in explicit forms are given and their properties are also analyzed. A bound solution without interaction will be theoretically predicted if one can adjust frequency shift for each soliton appropriately. Further, we obtain the approximate eigenvalues by employing two-soliton solution and discuss analytically the interaction between neighboring solitons under the influence of the higher-order effects. It is shown that the combined effects of the higher-order effects can restrain the interaction between neighboring solitons to some extent. The results are proved by directly solving HNLS equation numerically. 相似文献
35.
36.
This paper undertakes a systematic treatment of the low regularity local wellposedness and ill-posedness theory in Hs andHs for semilinear wave equations with polynomial nonlinearity in u and (e)u. This ill-posed result concerns the focusing type equations with nonlinearity on u and (e)tu. 相似文献
37.
38.
We establish a relation between stable distributions in probability theory and the fractional integral. Moreover, it turns out that the parameter of the stable distribution coincides with the exponent of the fractional integral. It follows from an analysis of the obtained results that equations with the fractional time derivative describe the evolution of some physical system whose time degree of freedom becomes stochastic, i.e., presents a sum of random time intervals subject to a stable probability distribution. We discuss relations between the fractal Cantor set (Cantor strips) and the fractional integral. We show that the possibility to use this relation as an approximation of the fractional integral is rather limited. 相似文献
39.
Geng Sheng WANG 《数学学报(英文版)》2005,21(5):1005-1014
This work is concerned with Pontryagin's maximum principle of optimal control problems governed by some non-well-posed semilinear heat equations. A type of approach to the non-well-posed optimal control problem is given. 相似文献
40.
李永祥 《数学物理学报(A辑)》2003,23(2):245-252
该文讨论四阶常微分方程边值问题u^(4)(t)=f(t,u,u″), t∈[0,1],u(0)=u(1)=u″(0)=u″(1)=0解的存在性, 其中f(t,u,v):[0,1]×R×R→R为Carathéodory函数. 在不限制f关于u,v的增长阶, 不假定f关于u,v的单调性的一般情形下, 用上下解方法获得了解的存在性结果,并讨论了单调迭代求解的有效性. 相似文献