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111.
Frank Natterer Olga Klyubina 《计算数学(英文版)》2007,25(3):368-373
We study the initial value problem of the Helmholtz equation with spatially variable wave number. We show that it can be stabilized by suppressing the evanescent waves. The stabilized Helmholtz equation can be solved numerically by a marching scheme combined with FFT. The resulting algorithm has complexity n^2 log n on a n x n grid. We demonstrate the efficacy of the method by numerical examples with caustics. For the Maxwell equation the same treatment is possible after reducing it to a second order system. We show how the method can be used for inverse problems arising in acoustic tomography and microwave imaging. 相似文献
112.
P. Kh. Atanasova T. L. Bojadjiev S. N. Dimova 《Computational Mathematics and Mathematical Physics》2006,46(4):666-679
Partial critical dependences of the form current-magnetic field in a two-layered symmetric Josephson junction are modeled. A numerical experiment shows that, for the zero interaction coefficient between the layers of the junction, jumps of the critical currents corresponding to different distributions of the magnetic fluxes in the layers may appear on the critical curves. This fact allows a mathematical interpretation of the results of some recent experimental results for two-layered junctions as a consequence of discontinuities of partial critical curves. 相似文献
113.
This paper is concerned with the existence of positive solutions of two-point Dirichlet singular and nonsingular boundary problems for second-order quasi-linear differential equations with changing sign nonlinearities. 相似文献
114.
In this paper, we discuss the dynamic behavior of networks of dynamic agents with general communication topologies. We first analyze the basic case: systems with communication topologies that have spanning trees, i.e., the systems that solve consensus problems. We establish an algebraic condition to characterize each agent's contributions to the final state. And we also study the influence of time-delays on each agent's contributions. Then, we investigate the general case: systems with weakly connected topologies. By using matrix theory, we prove that the states of internal agents will converge to a convex combination of boundary agents in the absence or presence of communication time-delays, and we also show that the coefficients of the convex combination are independent of time-delays even if the delays are time-varying. These results have broad applications in other areas, e.g., study of swarm behavior, formation control of vehicles, etc. 相似文献
115.
T. Linss 《BIT Numerical Mathematics》2007,47(2):379-391
A non-monotone FEM discretization of a singularly perturbed one-dimensional reaction-diffusion problem whose solution exhibits
strong layers is considered. The method is shown to be maximum-norm stable although it is not inverse monotone. Both a priori
and a posteriori error bounds in the maximum norm are derived. The a priori result can be used to deduce uniform convergence
of various layer-adapted meshes proposed in the literature. Numerical experiments complement the theoretical results.
AMS subject classification (2000) 65L10, 65L50, 65L60 相似文献
116.
Summary Equilibrium equations and stability conditions for the simple deformable elastic body are derived by means of considering
a minimum of the static energy principle. The energy is supposed to be sum of the volume (elastic) and the surface terms.
The ability to change relative positions of different material particles is taken into account, and appropriate natural definitions
of the first and second variations of the energy are introduced and calculated explicitly. Considering the case of negligible
magnitude of the surface tension, we establish that an equilibrium state of a nonhydrostatically stressed simple elastic body
(of any physically reasonable elastic energy potential and of any symmetry) possessing any small smooth part of free surface
is always unstable with respect to relative transfer of the material particles along the surface. Surface tension suppresses
the mentioned instability with respect to sufficiently short disturbances of the boundary surface and thus can probably provide
local smoothness of the equilibrium shape of the crystal. We derive explicit formulas for critical wavelength for the simplest
models of the internal and surface energies and for the simplest equilibrium configurations. We also formulate the simplest
problem of mathematical physics, revealing peculiarities and difficulties of the problem of equilibrium shape of elastic crystals,
and discuss possible manifestations of the above-mentioned instability in the problems of crystal growth, materials science,
fracture, physical chemistry, and low-temperature physics. 相似文献
117.
关于非线性Schrodinger方程混合问题解的破裂和质量集中 总被引:1,自引:0,他引:1
本文讨论了一类非线性Schrodinger方程混合问题解的破裂现象,blow-up时刻的估计和质量集中定理,并推广和改进了[l~3]中的结果. 相似文献
118.
In this paper, we treat a domain optimization problem in which the boundary-value problem is a Neumann problem. In the case where the domain is in a three-dimensional Euclidean space, the first-order and the second-order necessary conditions which the optimal domain must satisfy are derived under a constraint which is the generalization of the requisite of constant volume.Portions of this paper were presented at the 13th IFIP Conference on System Modelling and Optimization, Tokyo, Japan, 1987. 相似文献
119.
We consider the Stackelberg problem corresponding to a two-player game in which one of the two players has the leadership in playing the game. We present a general approach for approximating the considered hierarchical programming problem by a sequence of two-level optimization problems. From a practical point of view, we also give some results for asymptotically Stackelberg approximating sequences and for problems with perturbed constraints.This paper is based upon results first presented at Journées Fermat: Mathematics for Optimization, Toulouse, France, May 1985. 相似文献
120.
In this paper, we identify a new class of stochastic linearconvex optimal control problems, whose solution can be obtained by solving appropriate equivalent deterministic optimal control problems. The term linear-convex is meant to imply that the dynamics is linear and the cost function is convex in the state variables, linear in the control variables, and separable. Moreover, some of the coefficients in the dynamics are allowed to be random and the expectations of the control variables are allowed to be constrained. For any stochastic linear-convex problem, the equivalent deterministic problem is obtained. Furthermore, it is shown that the optimal feedback policy of the stochastic problem is affine in its current state, where the affine transformation depends explicitly on the optimal solution of the equivalent deterministic problem in a simple way. The result is illustrated by its application to a simple stochastic inventory control problem.This research was supported in part by NSERC Grant A4617, by SSHRC Grant 410-83-0888, and by an INRIA Post-Doctoral Fellowship. 相似文献