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951.
We consider a model for robust network design in telecommunications, in which we minimize the cost of the maximum mismatch between supply and demand. In the present study, the demand is uncertain and takes its values in a polytope defined by constraints. This problem is hardly tractable, so we limit ourselves to computing lower bounds (by a column-generation mechanism) and upper bounds (using an algorithm due to Falk and Soland for maximizing a separable convex function over a polytope). The experimental gap obtained turns out to be large, and this seems to be mainly due to poor upper bounds. Two possible solutions are suggested for further research aimed at improving them: dc optimization (to minimize the difference of two convex functions) and AARC modeling (affinely adjustable robust counterpart). 相似文献
952.
Degenerate parabolic equations of Kolmogorov type occur in many areas of analysis and applied mathematics. In their simplest form these equations were introduced by Kolmogorov in 1934 to describe the probability density of the positions and velocities of particles but the equations are also used as prototypes for evolution equations arising in the kinetic theory of gases. More recently equations of Kolmogorov type have also turned out to be relevant in option pricing in the setting of certain models for stochastic volatility and in the pricing of Asian options. The purpose of this paper is to numerically solve the Cauchy problem, for a general class of second order degenerate parabolic differential operators of Kolmogorov type with variable coefficients, using a posteriori error estimates and an algorithm for adaptive weak approximation of stochastic differential equations. Furthermore, we show how to apply these results in the context of mathematical finance and option pricing. The approach outlined in this paper circumvents many of the problems confronted by any deterministic approach based on, for example, a finite-difference discretization of the partial differential equation in itself. These problems are caused by the fact that the natural setting for degenerate parabolic differential operators of Kolmogorov type is that of a Lie group much more involved than the standard Euclidean Lie group of translations, the latter being relevant in the case of uniformly elliptic parabolic operators. 相似文献
953.
Jehad O. Alzabut 《Journal of Computational and Applied Mathematics》2010,234(1):233-2097
By means of the contraction mapping principle and Gronwall-Bellman’s inequality, we prove the existence and exponential stability of positive almost periodic solution for an impulsive delay Nicholson’s blowflies model. The main results are illustrated by an example. 相似文献
954.
Juan Carlos De los Reyes Sergio González Andrade 《Journal of Computational and Applied Mathematics》2010,235(1):11-32
This paper is devoted to the numerical simulation of two-dimensional stationary Bingham fluid flow by semismooth Newton methods. We analyze the modeling variational inequality of the second kind, considering both Dirichlet and stress-free boundary conditions. A family of Tikhonov regularized problems is proposed and the convergence of the regularized solutions to the original one is verified. By using Fenchel’s duality, optimality systems which characterize the original and regularized solutions are obtained. The regularized optimality systems are discretized using a finite element method with (cross-grid P1)-Q0 elements for the velocity and pressure, respectively. A semismooth Newton algorithm is proposed in order to solve the discretized optimality systems. Using an additional relaxation, a descent direction is constructed from each semismooth Newton iteration. Local superlinear convergence of the method is also proved. Finally, we perform numerical experiments in order to investigate the behavior and efficiency of the method. 相似文献
955.
In this paper, we investigate the initial-boundary problem of a degenerate parabolic system with nonlinear localized sources. We classify the blow-up solutions into global blow-up cases and single-point blow-up cases according to the values of m,n,pi,qi. Furthermore, we obtain the uniform blow-up profiles of solutions for the global blow-up case. Finally, we give some numerical examples to verify the results. These extend and generalize a recent work of one of the authors [L. Du, Blow-up for a degenerate reaction-diffusion systems with nonlinear localized sources, J. Math. Anal. Appl. 324 (2006) 304-320], which only considered uniform blow-up profiles under the special case p1=p2=0. 相似文献
956.
Bao-Feng Feng Ken-ichi Maruno 《Journal of Computational and Applied Mathematics》2010,235(1):229-5416
A self-adaptive moving mesh method is proposed for the numerical simulations of the Camassa-Holm equation. It is an integrable scheme in the sense that it possesses the exact N-soliton solution. It is named a self-adaptive moving mesh method, because the non-uniform mesh is driven and adapted automatically by the solution. Once the non-uniform mesh is evolved, the solution is determined by solving a tridiagonal linear system. Due to these two superior features of the method, several test problems give very satisfactory results even if by using a small number of grid points. 相似文献
957.
The dual conservation laws of elasticity are systematically re-examined by using both Noether's variational approach and Coleman–Noll–Gurtin's thermodynamics approach. These dual conservation laws can be interpreted as the dual configurational force, and therefore they provide the dual energy–momentum tensor. Some previously unknown and yet interesting results in elasticity theory have been discovered. As an example, we note the following duality condition between the configuration force (energy–momentum tensor) and the dual configuration force (dual energy–momentum tensor) ,
This and other results derived in this paper may lead to a better understanding of configurational mechanics and therefore of mechanics of defects. 相似文献
958.
Reinhard Farwig Giovanni P. Galdi Hermann Sohr 《Journal of Mathematical Fluid Mechanics》2006,8(3):423-444
We investigate a class of weak solutions, the so-called very weak solutions, to stationary and nonstationary Navier–Stokes equations in a bounded domain
. This notion was introduced by Amann [3], [4] for the nonstationary case with nonhomogeneous boundary data leading to a very
large solution class of low regularity. Here we are mainly interested in the investigation of the “largest possible” class
of solutions u for the more general problem with arbitrary divergence k = div u, boundary data g = u|∂Ω and an external force f, as weak as possible, but maintaining uniqueness. In principle, we will follow Amann’s approach. 相似文献
959.
Vasilii V. Kurta 《Archiv der Mathematik》2006,87(4):368-374
We generalize and improve recent non-existence results for global solutions to the Cauchy problem for the inequality
as well as for the equation ut = Δu + |u|q in the half-space
.
Received: 16 September 2005 相似文献
960.
Let F be the class of all 1-periodic real functions with absolutely convergent Fourier series expansion and let (xn)n ≧ 0 be the van der Corput sequence. In this paper results on the boundedness of
are given. We give a criterion on the convergence rate of the Fourier coefficients of f such that the above sum is bounded independently of N. Further we show that our result is also best possible.
The first author is supported by the Australian Research Council under its Center of Excellence Program. The second author
is supported by the Austrian Research Foundation (FWF), Project S9609 that is part of the Austrian National Research Network
“Analytic Combinatorics and Probabilistic Number Theory”.
Received: 14 December 2005 相似文献