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981.
In this article, we propose a tailored finite point method (TFPM) for the numerical solution of a type of fourth‐order singular perturbation problem in two dimensions based on the equation decomposition technique. Our finite point method has been tailored based on the local exponential basis functions. Furthermore, our TFPM satisfies the discrete maximum principle automatically. Our numerical examples show that our method has second order convergence rate in energy norm as $\varepsilon\to0$ . © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011 相似文献
982.
983.
Bing Sun 《Nonlinear Analysis: Real World Applications》2012,13(1):325-332
In this paper, the optimal distributed control of the viscous Dullin-Gottwald-Holm equation is investigated. Adopting the Dubovitskii and Milyutin functional analytical approach, we obtain the Pontryagin maximum principle of the system. The necessary optimality condition is established for an optimal control problem in fixed final horizon case. Finally, an illustrative example is also given. 相似文献
984.
《复变函数与椭圆型方程》2012,57(9):739-752
This article deals with the solvability of the CR equation rw = (A0(θ) ? O(rα))w ? (B0(θ) ? O(rα)), where z = r eiθ and where A0, B0 are continuous and 2π-periodic. The solutions of this equation are shown to be similar to those of the model equation rw = A0(θ)w ? B0(θ). The solutions of the model equation are completely characterized by using dynamical systems and Fourier techniques. 相似文献
985.
We briefly discuss the current status of Mach's principle in general relativity and point out that its last vestige, namely, the gravitomagnetic field associated with rotation, has recently been measured for the earth in the GP‐B experiment. Furthermore, in his analysis of the foundations of Newtonian mechanics, Mach provided an operational definition for inertial mass and pointed out that time and space are conceptually distinct from their operational definitions by means of masses. Mach recognized that this circumstance is due to the lack of any a priori connection between the inertial mass of a body and its Newtonian state in space and time. One possible way to improve upon this situation in classical physics is to associate mass with an extra dimension. Indeed, Einstein's theory of gravitation can be locally embedded in a Ricci‐flat 5D manifold such that the 4D energy‐momentum tensor appears to originate from the existence of the extra dimension. An outline of such a 5D Machian extension of Einstein's general relativity is presented. 相似文献
986.
Fractional differential equations of motion in terms of combined Riemann—Liouville derivatives 下载免费PDF全文
In this paper,we focus on studying the fractional variational principle and the differential equations of motion for a fractional mechanical system.A combined Riemann-Liouville fractional derivative operator is defined,and a fractional Hamilton principle under this definition is established.The fractional Lagrange equations and the fractional Hamilton canonical equations are derived from the fractional Hamilton principle.A number of special cases are given,showing the universality of our conclusions.At the end of the paper,an example is given to illustrate the application of the results. 相似文献
987.
The Pauli principle is included in a multisubband deterministic solver for two-dimensional devices without approximations.The nonlinear Boltzmann equations are treated properly without compromising on accuracy,convergence,or CPU time.The simulation results indicate the significant impact of the Pauli principle on the transport properties of the quasi-2D electron gas,especially for the on state. 相似文献
988.
Base force element method of complementary energy principle for large rotation problems 总被引:1,自引:0,他引:1
Using the concept of the base forces, a new finite element method (base force element method, BFEM) based on the complementary energy principle is presented for accurate modeling of structures with large displacements and large rotations. First, the complementary energy of an element is described by taking the base forces as state variables, and is then separated into deformation and rotation parts for the case of large deformation. Second, the control equations of the BFEM based on the complementary energy principle are derived using the Lagrange multiplier method. Nonlinear procedure of the BFEM is then developed. Finally, several examples are analyzed to illustrate the reliability and accuracy of the BFEM. 相似文献
989.
990.
After introducing some of the basic definitions and results
from the theory of groupoid and Lie algebroid, we investigate the
discrete Lagrangian mechanics from the viewpoint of groupoid theory
and give the connection between groupoids variation and the methods
of the first and second discrete variational principles. 相似文献