Méthode des éléments finis multi-échelles pour le problème de Stokes

This work consists of a numerical study of a multi-scale finite element method for a Stokes-type problem with highly oscillating coefficients. The objective of this method is to capture the multi-scale structure of the solution via local basis functions calculated in advance, which contain the essential information on small scales.     

Local energy decay for the wave equation with a nonlinear time-dependent damping

This article addresses a wave equation on a exterior domain in ? ^d (d odd) with nonlinear time-dependent dissipation. Under a microlocal geometric condition we prove that the decay rates of the local energy functional are obtained by solving a nonlinear non-autonomous differential equation     

Continuous location of an assembly station

Demand existing at client points in the plane for several products should be met. Products have to be assembled from different components obtainable at given prices at various sources with known production capacities. The optimal design of the resulting supply chain must be determined, including the location of a central assembly station in the plane, so as to minimize the total operational cost comprising buying and transport of components as well as transport of final products. This problem leads to a difficult nonlinear and non-convex optimization problem for which a locally convergent algorithm is proposed. Some computational results are presented.     

On Monotonic Integrable Solutions for Quadratic Functional Integral Equations

We study the solvability of functional quadratic integral equations in the space of integrable functions on the interval I = [0, 1]. We concentrate on a.e. monotonic solutions for considered problems. The existence result is obtained under the assumption that the functions involved in the investigated equation satisfy Carathéodory conditions. As a solution space we consider both L ₁(I) and L _p (I) spaces for p > 1.     

A scenario decomposition algorithm for 0–1 stochastic programs

We propose a scenario decomposition algorithm for stochastic 0–1 programs. The algorithm recovers an optimal solution by iteratively exploring and cutting-off candidate solutions obtained from solving scenario subproblems. The scheme is applicable to quite general problem structures and can be implemented in a distributed framework. Illustrative computational results on standard two-stage stochastic integer programming and nonlinear stochastic integer programming test problems are presented.     

A benders decomposition approach for an integrated airline schedule design and fleet assignment problem with flight retiming, schedule balance, and demand recapture

The airline’s ability to offer flight schedules that provide service to passengers at desired times in competitive markets, while matching demand with an aircraft fleet of suitable size and composition, can significantly impact its profits. In this spirit, optional flight legs can be considered to construct a profitable schedule by optimally selecting among such alternatives in concert with assigning the available aircraft fleet to all the scheduled legs. Examining itinerary-based demands as well as multiple fare-classes can effectively capture network effects and realistic demand patterns. In addition, allowing flexibility on the departure times of scheduled flight legs can increase connection opportunities for passengers, hence yielding robust schedules while saving fleet assignment costs within the framework of an integrated model. Airlines can also capture an adequate market share by balancing flight schedules throughout the day, and recapture considerations can contribute to more realistic accepted demand realizations. We therefore propose in this paper a model that integrates the schedule design and fleet assignment processes while considering flexible flight times, schedule balance, and recapture issues, along with optional legs, path/itinerary-based demands, and multiple fare-classes. A polyhedral analysis is conducted to generate several classes of valid inequalities, which are used along with suitable separation routines to tighten the model representation. Solution approaches are designed by applying Benders decomposition method to the resulting tightened model, and computational results are presented using real data obtained from United Airlines to demonstrate the efficacy of the proposed procedures.     

The numerical index of the space

We give a partial answer to the problem of computing the numerical index of for .

     

Exponential Attractor for a Nonlinear Boussinesq Equation

This paper is devoted to prove the existence of an exponential attractor for the semiflow generated by a nonlinear Boussinesq equation. We formulate the Boussinesq equation as an abstract equation in the Hilbert space H0^2（0, 1） × L^2（0, 1）. The main step in this research is to show that there exists an absorbing set for the solution semiflow in the Hilbert space H0^3（0, 1） × H0^1（0, 1）.     

On the Theta Semigroup

In this paper we consider a semigroup on trigonometric expansions ${\{{\mathcal T}_t: t \geq 0\}}$ that will be called the Theta semigroup since its kernel is a multiple of ?? ₃(x, q), the third Jacobi theta function. We study properties of this semigroup and prove that it is a positive diffusion semigroup. We also obtain that its subordinated semigroup is the classical Poisson semigroup. The extensions to higher dimensions and to periodic ultra distributions are also considered.