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Journal of Partial Differential Equations 2024年第1期37卷 1-24页

作者： MALIKI Youssef TERKI Fatima Zohra laboratoire systemes dynamiques et Applications department of Mathematics `University Aboubekr Belka¨id of TlemcenTlemcenAlgeria.

We prove the existence of multiple solutions of an elliptic equation with critical Sobolev growth and critical Hardy potential on compact Riemannian manifolds.

关键词： Riemannian manifolds Yamabe equation Hardy potential.

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

Analysis of a quasistatic contact problem with adhesion and nonlocal friction for viscoelastic materials

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Applied Mathematics and Mechanics(English Edition) 2010年第5期31卷 623-634页

作者： Arezki TOUZALINE laboratoire de systèmes dynamiques Facult de Mathmatiques Universit des Sciences et de la Technologie Houari Boumediene

A mathematical model is established to describe a contact problem between a deformable body and a foundation. The contact is bilateral and modelled with a nonlocal friction law, in which adhesion is taken into account. Evolution of the bonding field is described by a first-order differential equation. The materials behavior is modelled with a nonlinear viscoelastic constitutive law. A variational formulation of the mechanical problem is derived, and the existence and uniqueness of the weak solution can be proven if the coefficient of friction is sufficiently small. The proof is based on arguments of time-dependent variational inequalities, differential equations, and the Banach fixed-point theorem.

关键词： viscoelastic materials adhesion nonlocal friction fixed point weak solution

Quantum-classical correspondence for the inverted oscillator

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Chinese Physics C 2017年第11期41卷 56-62页

作者： Mustapha Maamache Jeong Ryeol Choi laboratoire de Physique Quantique et systèmes dynamiques Faculté des SciencesUniversité Ferhat Abbas Sétif 1 Sétif 19000 department of Radiologic Technology Daegu Health College

While quantum-classical correspondence for a system is a very fundamental problem in modern physics,the understanding of its mechanism is often elusive,so the methods used and the results of detailed theoretical analysis have been accompanied by active *** this study,the differences and similarities between quantum and classical behavior for an inverted oscillator have been analyzed based on the description of a complete generalized Airy function-type quantum wave *** inverted oscillator model plays an important role in several branches of cosmology and particle *** quantum wave packet of the system is composed of many sub-packets that are localized at different positions with regular intervals between *** is shown from illustrations of the probability density that,although the quantum trajectory of the wave propagation is somewhat different from the corresponding classical one,the difference becomes relatively small when the classical excitation is sufficiently *** have confirmed that a quantum wave packet moving along a positive or negative direction accelerates over time like a classical *** these main interpretations and others in the text,we conclude that our theory exquisitely illustrates quantum and classical correspondence for the system,which is a crucial concept in quantum mechanics.

关键词： quantum-classical correspondence inverted oscillator quantum wave packet

Nonlinear description of Yang-Mills cosmology： cosmic inflation and the accompanying Hannay's angle

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Chinese Physics C 2017年第6期41卷 115-121页

作者： Yacine Bouguerra Mustapha Maamache Jeong Ryeol Choi laboratoire de Physique Quantique et systèmes dynamiques Faculté des SciencesUniversite Ferhat Abbas Setif 1 Setif 19000 Algeria Département de Physique Facultédes Sciences Université de Jijel BP 98Ouled Aissa Jijel 18000 Algeria department of Radiologic Technology Daegu Health College Yeongsong-ro 15 Buk-gu Daegu 41453 Republic of Korea

Hannay＇s angle is a classical analogue of the ＂geometrical phase factor＂ found by Berry in his research on the quantum adiabatic theorem. This classical analogue is defined if closed curves of constant action variables return to the same curves in phase space after an adaibatic evolution. Adiabatic evolution of Yang-Mills cosmology, which is described by a time-dependent quartic oscillator, is investigated. Phase properties of the Yang-Mills fields are analyzed and the corresponding Hannay＇s angle is derived from a rigorous evaluation. The obtained Hannay＇s angle shift is represented in terms of several observable parameters associated with such an angle shift. The time evolution of Hannay＇s angle in Yang-Mills cosmology is examined from an illustration plotted on the basis of numerical evaluation,and its physical nature is addressed. Hannay＇s angle, together with its quantum counterpart Berry＇s phase, plays a pivotal role in conceptual understanding of several cosmological problems and indeed can be used as a supplementary probe for cosmic inflation.

关键词： Yang-Mills cosmology Hannay angle time-dependent quartic Hamiltnian inflation

ON A SECOND ORdeR DISSIPATIVE Ode IN HILBERT SPACE WITH AN INTEGRABLE SOURCE TERM

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Acta Mathematica Scientia 2012年第1期32卷 155-163页

作者： Alain Haraux Mohamed Ali Jendoubi UPMC Univ Paris 06 UMR 7598Laboratoire Jacques-Louis Lions CNRS UMR 7598Laboratoire Jacques-Louis Lions Facult des Sciences de Bizerte Dpartement de Mathmatiques

Asymptotic behaviour of solutions is studied for some second order equations including the model casex（t）＋γx（t）＋ ↓△φb（x（t）） = h（t） with γ 〉 0 and h ∈ L1（O, ＋∞; H）, φ being continuouly differentiable with locally Lipschitz continuous gradient and bounded from below. In particular when φ is convex, all solutions tend to minimize the potential φ as time tends to infinity and the existence of one bounded trajectory implies the weak convergence of all solutions to equilibrium points.

关键词： dissipative dynamical system asymptotic behaviour gradient system heavyball with friction

The Evolution of Pore Water Pressure in a Saturated Soil Layer between Two Draining Zones by Analytical and Numerical Methods

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Open Journal of Civil Engineering 2015年第4期5卷 390-398页

作者： Abib Tall Cheikh Mbow Daouda Sangaré Mapathé Ndiaye Papa Sanou Faye laboratoire de Mé canique et Modé lisation UFR Sciences de l’Ing&eacute nieur Univer-sit&eacute de Thiè s Thi&egrave s S&eacute né gal Groupe de Recherches sur les dynamiques des systè mes et la Mé canique des Fluides Fac-ult&eacute des Sciences et Techniques Universit&eacute Cheikh Anta Diop Dakar S&eacute né gal laboratoire d’Analyse Numé rique et d’Informatique UFR Sciences Appliqu&eacute es et Technologie Universit&eacute

The building of the infrastructure on the compressible and saturated soils presents sometimes major difficulties. The infrastructure undergoes strong settlement that can be due to several phenomena of consolidation of the soils. The latter results from the dissipation of the excess pore pressure and deformation of the solid skeleton. Terzaghi theory led to the equation modeling the dissipation of excess pore pressure. The objective of this study is to establish solutions, by analytical and numerical method, of the equation of the pore water pressure. We considered a compressible saturated soil layer, between two drainage areas and subjected to a uniform load. Separation of variables is used to obtain an analytical solution and the finite element method for the numerical solution. The results obtained by the finite element method have validated those of analytical resolution.

关键词： Pore Water Pressure Primary Consolidation Saturated Soil Separated Variables Finite Element

Inoculation of <i>Rhizobiums sp</i>Strains to Improve Soil Fertility: A Peanut Trial in Covèand Ouessè(Benin)

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Agricultural Sciences 2020年第4期11卷 448-463页

作者： Alida Adjile Oscar Didagbe Carrel Ayelo Frechno Boko Pascal Houngnandan Roch Mongbo laboratoire d’Analyse des dynamiques Sociales et des Etudes du Développement (LADYD) Faculté des Sciences Agronomiques Université d’Abomey-Calavi Abomey-Calavi Bénin laboratoire de Microbiologie des Sols et d’Ecologie Microbienne Faculté des Sciences Agronomiques Université d’Abomey-Calavi Abomey-Calavi Bénin laboratoire de Biologie et de Typage Moléculaire en Microbiologie Faculté des Sciences et Techniques Université d’Abomey-Calavi Abomey-Calavi Bénin

Thought the increasing demand Arachis hypogaea L. (groundnut), its yields remain low with increasingly using chemical fertilizers. To reduce the costs for chemical fertilizers inquisition and their long-term toxic effects on soils, microbial bio-fertilizers could be an accessible alternative to peanut farms. Thus, the aim of this study was to assess the performance of rhizobia strains on peanut varieties production. The experiments were conducted in two agro-ecological zones of Benin, in a peasant environment peasant-researcher control or under peasant and researcher control. The experimental device used was a complete random block with nine repetitions and two factors namely inoculation (with Rhizobium sp and without Rhizobium sp) and mineral fertilizer (with N15P15K15 and without N15P15K15). The effects of these factors divided into four treatments were evaluated on the plants vegetative, symbiotic and production parameters. In addition, an evaluation of each treatments’ comparative advantages was carried out. The results showed that the association Rhizobium sp and N15P15K15 induced groundnut plants best vegetative and productive parameters. The best comparative advantages in economic terms were also recorded with the same combination (Rhizobium sp + N15P15K15). Considering the technical performance, the recorded treatments effects can be classified as follows: Control Rhizobium sp 15P15K15 Rhizobium sp + N15P15K15. Thus, the association Rhizobium sp + N15P15K15 induced both the best plants vegetative and productive parameters and the best comparative advantage from an economic point of view. The results also showed that the plants’ response to inoculation, the application of manure and their combination was more marked in the bar soil zone (Covè) than in the cotton zone (Ouessè). Considering the negative effects linked to the use of chemical fertilizers, the use of Rhizobium sp could be an interesting path to increase the groundnut production.

关键词： Arachis hypogeae L. Rhizobium sp Bio Fertilizer Soil Fertility Benin