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Numerical Study of Semidiscrete Penalty Approach for Stabilizing Boussinesq System with Localized Feedback Control

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Annals of Applied Mathematics 2024年第2期40卷 191-218页

作者： Mejdi Azaiez Kevin Le Balc'h Universite de Bordeaux Bordeaux-INPI2M UMR5295F-33400TalenceFrance Inria Sorbonne UniversiteUniversite de ParisCNRSLaboratoire Jacques-Louis LionsParisFrance

We investigate the numerical approximation for stabilizing the semidiscrete linearized Boussinesq system around an unstable stationary *** is attained through internal feedback controls applied to the velocity and temperature equations,localized within an arbitrary open *** study follows the framework presented in[14],considering the continuous linearized Boussinesq *** primary objective is to explore the penalizationbased approximation of the free divergence condition in the semidiscrete case and provide a numerical validation of these results in a two-dimensional setting.

关键词： Boussinesq system penalty method stabilization feedback control

REITERATED HOMOGENIZATION OF DEGENERATE NONLINEAR ELLIPTIC EQUATIONS

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Chinese Annals of Mathematics,Series B 2002年第3期23卷 325-334页

作者： J.BYSTRM J.ENGSTRM P.WALL Dedicated to the memory of jacques-Louis Lions Dedicated to the memory of Jacques-Louis LionsDedicated to the memory of Jacques-Louis Lions

The authors study homogenization of some nonlinear partial differential equations of the form -div (a (hx, h^2x, Duh))=f, where a is periodic in the first two arguments and monotone in the third. In particular the case where a satisfies degenerated structure conditions is *** is proved that uh converges weakly in W0^1,1 (Ω) to the unique solution of a limit problem as h→＋∞. Moreover, explicit expressions for the limit problem are obtained.

关键词：反复齐次化退化非线性椭圆方程偏微分算子单调性周期性 Dirichlet问题齐次算子

ON THE UNIQUENESS OF THE WEAK SOLUTIONS OF A QUASILINEAR HYPERBOLIC SYSTEM WITH A SINGULAR SOURCE TERM

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Chinese Annals of Mathematics,Series B 2002年第3期23卷 317-324页

作者： J.P.DIAS M.FIGUEIRA Dedicated to the memory of jacques-Louis Lions Dedicated to the memory of Jacques-Louis Lions

This paper is a continuation of the authors' previous paper [1].In this paper the authors prove,assuming additional conditions on the initial data,some results about the existence and uniqueness of the entropy weak solutions of the Cauchy problem for the singular hyperbolic system at + (au)x + 2aux = 0, x＞0,t≥0. ut + 1/2 (a2 + u2)x = o,

关键词：唯一性弱熵解拟线性双曲系统奇异源项 Cauchy问题 Riemann边分抛物系统

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皮亚杰错了吗?

华东师范大学学报(教育科学版) 2000年第3期 47-52页

作者：弗内歇熊哲宏 jacques vonèche 日内瓦大学心理学系教授、皮亚杰档案馆馆长

本文依据皮亚杰的经典理论,对某些旨在否定皮亚杰理论的实验及其解释作了深刻的反思和批评,从而表明皮亚杰理论仍然具有很强的生命力。

关键词：客体永久性分类序列化数守恒去中心化社会相互作用

Art of Nourishing Life According to the Kidney Meridian in Zhenjiu Dacheng(The Great Compendium of Acupuncture and Moxibustion)

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Chinese Medicine and Culture 2022年第2期5卷 91-96页

作者： Anita Bui Faculty of Medicine of Sorbonne University Paris 75005France Saint jacques Health Center Paris 75015France

“Daoyin Benjing”(Art of Nourishing Life)discusses the kidney meridian in *** is a dense and heterogeneous text that is heavily influenced by *** text proposes rules for the maintenance of life using language that is often cryptic and under-standable only to the *** language is closely interwoven with the classical terms of traditional Chinese *** kidney is the home of vital energy,which is a type of sexual energy and the root of *** in moderate sexual activity nourishes life and leads to a long *** is the goal of every Daoist follower and the goal of every doctor.

关键词： Daoyin Kidney Art of nourishing life Yang Jizhou The Great Compendium of Acupuncture and Moxibustion

SENSITIVITY OF DARCY'S LAW TO DISCONTINUITIES

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Chinese Annals of Mathematics,Series B 2003年第2期24卷 205-214页

作者： C.BERNARDI O.PIRONNEAU Laboratoie jacques-Louis Lions Universite Paris VI-CNRSFrance.Laboratorie Jacques-Louis LionsUniversite Paris VI-IUFFrance.

The authors investigate the sensitivity of hydrostatic pressure of flows through porous mediawith respect to the position of the soil layers. Indeed, these induce discontinuities of the porositypressure u and it leads to the computation of the derivative of u with respect to changes inThe analysis relies on a mixed formulation of the problem. Preliminary numerical simu-lations are given to illustrate the theory. An application to a simple inverse problem is also given.

关键词：灵敏度 Darcy律偏微分方程多孔介质流体静力压力不连续性混合公式导数存在性唯一性正则性可微性

Modelling of Electrical Conductivity of a Silver Plasma at Low Temperature

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Plasma Science and Technology 2016年第8期18卷 812-820页

作者： Pascal ANDRE William BUSSIERE Alain COULBOIS Jean-Louis GELET David ROcheTTE Université Clermont Auvergne LAEPT MERSEN 15 rue Jacques de Vaucanson

During the working of electrical fuses, inside the fuse element the silver ribbon first begins to melt, to vaporize and then a fuse arc appears between the two separated parts of the element. Second, the electrodes are struck and the burn-back phenomenon takes place. Usually, the silver ribbon is enclosed inside a cavity filled with silica sand. During the vaporization of the fuse element, one can consider that the volume is fixed so that the pressure increase appears to reach pressures higher than atmospheric pressure. Thus, in this paper two pressures, 1 atm and 10 atm, are considered. The electrical field inside the plasma can reach high values since the distance between the cathode surface and the anode surface varies with time. That is to say from zero cm to one cm order. So we consider various electrical fields： 102 V/m, 103 V/m, 5×103 V/m, 104 V/m at atmospheric pressure and 105 V/m at a pressure of 10 atm. This study is made in heavy species temperature range from 2,400 K to 10,000 K. To study the plasma created inside the electric fuse, we first need to determine some characteristics in order to justify some hypotheses. That is to say： are the classical approximations of the thermal plasmas physics justified？ In other words： plasma frequency, the ideality of the plasma, the Debye-Hückel approximation and the drift velocity versus thermal velocity. These characteristics and assumptions are discussed and commented on in this paper. Then, an evaluation of non-thermal equilibrium versus considered electrical fields is given. Finally, considering the high mobility of electrons, we evaluate the electrical conductivities.

关键词： electrical conductivity silver fuses non-ideal plasma Debye-Hiickelapproximation drift velocity thermal velocity thermal non-equilibrium electrical fields

Nonlinear Shell Models of Kirchhoff-Love Type:Existence Theorem and Comparison with Koiter's Model

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Acta Mathematicae Applicatae Sinica 2019年第1期35卷 3-27页

作者： Cristinel MARDARE Sorbonne Université CNRS Laboratoire Jacques-Louis LionsLJLL

We define two nonlinear shell models whereby the deformation of an elastic shell with small thickness minimizes ad hoc functionals over sets of admissible deformations of Kirchhoff-Love type. We establish that both models are close in a specific sense to the well-known nonlinear shell model of W.T. Koiter and that one of them has a solution, by contrast with Koiter's model for which such an existence theorem is yet to be proven.

关键词： Nonlinearly Elastic Shells Kirchhoff-Love Koiter Existence Theory Asymptotics

Analysis of Lateritic Soil Reinforced with Palm Kernel Shells for Use as a Sub-Base Layer for Low-Traffic Roads

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Fluid Dynamics & Materials Processing 2022年第5期18卷 1469-1482页

作者： Joel Koti Crespin P.Yabi Mohamed Gibigaye Anne Millien Christophe Petit LEMA University of Abomey-CalaviCotonouBenin GC2D University of Limoges17 Bd Jacques DercheEgletonsFrance National University of Sciences TechnologiesEngineering and MathematicsAbomeyBenin

In tropical areas,palm oil production generates significant amounts of waste,including palm kernel *** use of this waste in the civil engineering sector,presents a very challenging *** the present study,the production of lateritic soil(A-2 in GTR classification and A-7-6(9)in HRB classification)reinforced with palm kernel shells is *** order to improve their performances,these materials are mixed using the Fuller’s parabolic ***,experimental tests are used to characterize the physical and mechanical geotechnical properties of the lateritic *** characterizing the matrix(i.e.,lateritic soil)and the inclusions(i.e.,palm kernel shells)in their natural state,it is found that Avrankou’s lateritic soil has a high level of fine particles(56.6%),high plasticity(PI=21%)and low lift(ICBR=17%);which makes it unusable in the pavement *** also prove that the mixture composed of 39%of lateritic soil volume and 61%of PKS with a CBR index equals to 30 and the mixture composed of 45%of lateritic soil,40%PKS and 15%of lagoon sand with a CBR index equals to 41 can be used as sub-base layer for roads for low and medium traffic,respectively.

关键词： Palm kernel shell lateritic soil subbase layer low-traffic roads