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CONJUGATE-SYMPLECTICITY OF LINEAR MULTISTEP METHODS

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Journal of Computational Mathematics 2008年第5期26卷 657-659页

作者： Ernst Hairer Section de Mathématiques Univ.de Genève

For the numerical treatment of Hamiltonian differential equations, symplectic integrators are the most suitable choice, and methods that are conjugate to a symplectic integrator share the same good long-time behavior. This note characterizes linear multistep methods whose underlying one-step method is conjugate to a symplectic integrator. The bounded- hess of parasitic solution components is not addressed.

关键词： Linear multistep method Underlying one-step method Conjugate-symplecticity,Symmetry.

Generalized Backward Doubly Stochastic Differential Equations Driven by Lévy Processes with Continuous Coefficients

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Acta Mathematica Sinica,English Series 2012年第10期28卷 2011-2020页

作者： Auguste AMAN Jean Marc OWO UFR de Mathématiques et Informatique Université de Cocody

A new class of generalized backward doubly stochastic differential equations （GBDSDEs in short） driven by Teugels martingales associated with Levy process are investigated. We establish a comparison theorem which al... 详细信息

关键词： Backward doubly stochastic differential equations L@vy processes Teugels martingales comparison theorem continuous and linear growth conditions

Optimal Control of a Frictional Contact Problem

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Acta Mathematicae Applicatae Sinica 2015年第4期31卷 991-1000页

作者： Arezki TOUZALINE Laboratoire de Systèmes Dynamiques Faculté de MathématiquesUSTHB

We consider a mathematical model which describes a contact between a deformable body and a foundation. The contact is bilateral and modelled with Tresca＇s friction law. The goal of this paper is to study an optimal control problem which consists of leading the stress tensor as close as possible to a given target, by acting with a control on the boundary of the body. We state an optimal control problem which admits at least one solution. We also introduce the regularized control problem for which we study the convergence when the regularization parameter tends to zero. Finally, an optimally condition is established for this problem.

关键词： optimal control of variational inequalities elastic materials Tresca's friction, weak solution

QUANTIZATION COMMUTES WITH REDUCTION,A SURVEY

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Acta Mathematica Scientia 2021年第6期41卷 1859-1872页

作者： Xiaonan MA Institut de Mathématiques de Jussieu-Paris Rive Gauche Universitéde ParisUFR de MathématiquesCase 701275205Paris Cedex 13France

We review the themes relating to the proposition that“quantization commutes with reduction”([Q,R]=0),from symplectic manifolds to Cauchy-Riemann manifolds.

关键词： index theory Dirac operator geometric quantization

EXISTENCE OF SOLUTIONS FOR GRADIENT SYSTEMS WITH APPLICATION TO DIFFUSION PROBLEMS INVOLVING NONCONVEX ENERGIES

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Acta Mathematica Scientia 2018年第6期38卷 1767-1778页

作者： Sahbi BOUSSANDEL Dpartement de Mathmatiques Facult des Sciences de Bizerte

In this paper, we establish the existence of solutions for gradient systems ofevolution under some type （M） and semi-coerciveness conditions. The main result is appliedin order to solve nonlinear diffusion equations... 详细信息

关键词： gradient systems existence of solutions Galerkin method type (M) condition semi-coerciveness diffusion equations

ASYMPTOTIC BEHAVIOR OF THE TE AND TM APPROXIMATIONS TO SECOND HARMONIC GENERATION

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Journal of Computational Mathematics 2007年第1期25卷 49-66页

作者： Na■ma A■ssa Faculté de Mathématiques USTHBBP32El AliaBab Ezzouar16111Alger Centre de Mathématiques Appliquées CNRS UMR 7641■Ecole PolytechniquePalaiseau 91128 CedexFrance

We consider a Second Harmonic Generation （SHG） problem of an optical signal wave with an optical pump in a medium represented by a smooth bounded domain Ω→∩ IR^d which is assumed to contain a heterogeneous material： a compactly imbedded subdomain B^r →∩∩ in the shape of a small ball contains a nonlinear material, while Ω／ B^r is filled with a linear material. We begin by proving existence and uniqueness of the solution to the TE approximation of SHG for arbitrary bounded susceptibilities, thus improving the result obtained by Bao and Dobson （ Eur. J. Appl. Math. 6 （1995）, 573-590） under small enough susceptibilities assuption. We then establish an existence and uniqueness result of a solution to the TM approximation problem. In both parts we study the asymptotic behavior of the system as the size of the nonlinear material vanishes： error estimates and asymptotic expansion of the solution are derived for both TE and TM approximations.

关键词： Second harmonic generation TE Approximation TM Approximation.

New Characterizations of the Dual Spaces of Hardy-amalgam Spaces

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Acta Mathematica Sinica,English Series 2022年第3期38卷 519-546页

作者： Zobo Vincent de Paul ABLE Justin FEUTO Laboratoire de Mathématiques Fondamentales UFR Mathématiques et InformatiqueUniversitéFélixHouphouët-Boigny Abidjan-Cocody22B.P.582Abidjan 22Côte d’Ivoire Laboratoire de Mathématiques Fondamentales UFR Mathématiques et InformatiqueUniversitéFélixHouphouët-Boigny Abidjan-Cocody22B.P.1194Abidjan 22Côte d’Ivoire

In this paper,carrying on with our study of the Hardy-amalgam spaces H^((q,p)) and H^((q,p))_(loc)(0 详细信息

In this paper,carrying on with our study of the Hardy-amalgam spaces H^((q,p)) and H^((q,p))_(loc)(0

关键词： Amalgam spaces Hardy-amalgam spaces duality Pseudo-differential operators

Sanya Lectures: Geometry of Spherical Varieties

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Acta Mathematica Sinica,English Series 2018年第3期34卷 371-416页

作者： Nicolas PERRIN Laboratoire de Mathématiques de Versailles UVSQ CNRS Université Paris-Saclay

These are expanded notes from lectures on the geometry of spherical varieties given in Sanya. We review some aspects of the geometry of spherical varieties. We first describe the structure of B-orbits. Using the local structure theorems, we describe the Picard group and the group of Weyl divisors and give some necessary conditions for smoothness. We later on consider B-stable curves and describe in details the structure of the Chow group of curves as well as the pairing between curves and divisors. Building on these results we give an explicit B-stable canonical divisor on any spherical variety.

关键词： Spherical varieties orbits local structure divisors curves

Dynamics of a rigid body in a two-dimensional incompressible perfect fluid and the zero-radius limit Dedicated to Professor Jean-Yves Chemin on the Occasion of His 60th Birthday

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Science China Mathematics 2019年第6期62卷 1205-1218页

作者： Franck Sueur Institut de Mathématiques de Bordeaux CNRS UMR 5251 Université de Bordeaux

In this survey we report some recent results on the dynamics of a rigid body immersed in a twodimensional incompressible perfect fluid, with an emphasis on the zero-radius limit.

关键词： fluid-structure interaction point vortex perfect incompressible fluid