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Inverse Scattering for a Schr■dinger Operator with a Repulsive Potential

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Acta mathematica Sinica,English Series 2006年第5期22卷 1485-1492页

作者： Francois NICOlEAU laboratoire de mathéatiques Jean leray UMR CNRS-UN 6629 Département de Mathématiques2 rue de la Houssinière BP 92208 F-44322 Nantes cedex 03 France

We consider a pair of Hamiltonians （H, H0） on l2（R^n）, where H0=p^2 -x^2 is a SchrSdinger operator with a repulsive potential, and H = H0＋V（x）. We show that, under suitable assumptions on the decay of the elect... 详细信息

关键词： Inverse scattering Repulsive potential

On the Stability of Racing Sailing Boats with Foils

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Chinese Annals of mathematics,Series B 2018年第3期39卷 427-450页

作者： Philippe deSTUYNdeR Caroline FABRE Département d'ingénierie mathématique Laboratoire M2N Conservatoire National des Arts et Métiers 292rue saint Martin75003 ParisFrance laboratoire de mathématiques d'Orsay Univ.Paris-SudCNRSUniversitéParis-Saclay 91405 OrsayFrance

The development of foils for racing boats has changed the strategy of sailing. Recently, the America＇s cup held in San Francisco, has been the theatre of a tragicomic history due to the foils. During the last round, the New-Zealand boat was winning by 8 to 1 against the defender USA. The winner is the first with 9 victories. USA team understood suddenly （may be） how to use the control of the pitching of the inain foils by adjusting the rake in order to stabilize the ship. And USA won by 9 victories against 8 to the challenger NZ. The goal in this paper is to point out few aspects which could be taken into account in order to improve this mysterious control law which is known as the key of the victory of the USA team. There are certainly many reasons and in particular the cleverness of the sailors and of all the engineering team behind this project. But it appears interesting to have a mathematical discussion, even if it is a partial one, on the mechanical behaviour of these extraordinary sailing boats. The nunlerical exanlples given here are not the true ones. They have just been invented in order to explain the theoretical developments concerning three points： The possibility of tacking on the foils for sailing upwind, the nature of foiling instabilities, if there are, when the boat is flying and the control laws.

关键词： Hydrodynamics of foils mathematical analysis Stability

Quasi-hydrostatic Primitive Equations for Ocean Global Circulation Models

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Chinese Annals of mathematics,Series B 2010年第6期31卷 939-952页

作者： Carine lUCAS Madalina PETCU Antoine ROUSSEAU laboratoire MAPMO (UMR 6628) Fédération Denis Poisson (FDP-FR2964) Université d'OrléansBtiment de Mathématiques-Route de Chartres B. P. 6759 45067 Orléans Cedex 2 France laboratoire de mathématiques et Applications Téléport 2-B. P. 30179 Boulevard Marie et Pierre Curie 86962 Futuroscope Chasseneuil Cedex France INRIA Laboratoire Jean Kuntzmann 51 rue des Mathématiques B. P. 53 38041 Grenoble Cedex 9France

Global existence of weak and strong solutions to the quasi-hydrostatic primitive equations is studied in this paper. This model, that derives from the full non-hydrostatic model for geophysical fluid dynamics in the zero-limit of the aspect ratio, is more realistic than the classical hydrostatic model, since the traditional approximation that consists in neglecting a part of the Coriolis force is relaxed. After justifying the derivation of the model, the authors provide a rigorous proof of global existence of weak solutions, and well-posedness for strong solutions in dimension three.

关键词： Hydrostatic approximation Coriolis force Ocean global circulation models Primitive equations Traditional approximation

lipschitz Properties in Variable Exponent Problems via Relative Rearrangement

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Chinese Annals of mathematics,Series B 2010年第6期31卷 991-1006页

作者： Jean-Michel RAKOTOSON UMR 6086 CNRS.laboratoire de mathématiques Université de Poitiers SP2MI Boulevard Marie et Pierre Curie Téléport 2 BP30179 86962 Futuroscope Chasseneuil Cedex France

The author first studies the lipschitz properties of the monotone and relative rearrangement mappings in variable exponent lebesgue spaces completing the result given in [9]. This paper is ended by establishing the lipschitz properties for quasilinear problems with variable exponent when the right-hand side is in some dual spaces of a suitable Sobolev space associated to variable exponent.

关键词： Monotone rearrangement Relative rearrangement Variable exponents Quasi-linear equations

ASYMPTOTIC BEHAVIOR OF GlOBAl SMOOTH SOlUTIONS FOR BIPOlAR COMPRESSIBlE NAVIER-STOKES-MAXWEll SYSTEM FROM PlASMAS

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Acta mathematica Scientia 2015年第5期35卷 955-969页

作者：冯跃红王术李新 College of Applied Sciences Beijing University of Technology laboratoire de mathématiques Université Blaise Pascal department of mathematics and Computer Science Xinyang Vocational and Technical College

This paper is concerned with the bipolar compressible Navier-Stokes-Maxwell system for plasmas. We investigated, by means of the techniques of symmetrizer and elaborate energy method, the Cauchy problem in R^3. Under the assumption that the initial values are close to a equilibrium solutions, we prove that the smooth solutions of this problem converge to a steady state as the time goes to the infinity. It is shown that the difference of densities of two carriers converge to the equilibrium states with the norm ｜｜·｜｜H^s-1, while the velocities and the electromagnetic fields converge to the equilibrium states with weaker norms than ｜｜·｜｜H^s-1. This phenomenon on the charge transport shows the essential difference between the unipolar Navier-Stokes-Maxwell and the bipolar Navier-Stokes-Maxwell system.

关键词： bipolar compressible Navier-Stokes-Maxwell system plasmas global smooth solutions energy estimates large-time behavior

ON THETA-TYPE FUNCTIONS IN THE FORM(x;q)∞

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Acta mathematica Scientia 2021年第6期41卷 2086-2106页

作者： Changgui ZHANG laboratoire P.Painlevé(UMR—CNRS 8524) Département de mathématiquesFSTUniversitéde LilleCitéscientifique59655Villeneuve d’Ascq cedexFrance

As in our previous work [14], a function is said to be of theta-type when its asymptotic behavior near any root of unity is similar to what happened for Jacobi theta functions. It is shown that only four Euler infinite products have this property. That this is the case is obtained by investigating the analyticity obstacle of a laplace-type integral of the exponential generating function of Bernoulli numbers.

关键词： q-series Mock theta-functions Stokes phenomenon continued fractions

The periodic unfolding method for the heat equation in perforated domains

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Science China mathematics 2016年第5期59卷 891-906页

作者： DONATO Patrizia YANG ZhanYing laboratoire de mathématiques Raphael Salem Normandie Université Université de Rouen Saint Etienne de Rouvray 76801 France department of mathematics South-Central University for Nationalities Wuhan 430074 China

We study the heat equation with non-periodic coefficients in periodically perforated domains with a homogeneous Neumann condition on the holes. Using the time-dependent unfolding method, we obtain some homogenization ... 详细信息

关键词： heat equations perforated domains homogenization correctors periodic unfolding method

ASYMPTOTIC lIMITS OF ONE-DIMENSIONAl HYDRODYNAMIC MOdelS FOR PlASMAS AND SEMICONDUCTORS

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Chinese Annals of mathematics,Series B 2002年第1期23卷 25-36页

作者： PENG YUEJUN laboratoire de mathematiques Appliquees, CNRS UMR 6620, Universite Blaise Pascal (Clermont-Ferrand 2), F-63177 Aubiere cedex, France. E-mail: peng@math.univ-bpclermont.fr laboratoire de mathématiques Appliquées CNRS UMR 6620 Université Blaise Pascal (Clermont-Ferrand 2) F-63177 Aubière cedex France

This paper studies the zero-electron-mass limit, the quasi-neutral limit and the zero-relaxation-time limit in one-dimensional hydrodynamic models of Euler-Poisson system for plasmas and semiconductors. For each limit in the steady-state models, the author proves the strong convergence of the sequence of solutions and gives the corresponding convergence rate. In the time-dependent models, the author shows some useful estimates for the quasi-neutral limit and the zero-electron-mass limit. This study completes the analysis made in [11,12,13,14,19].

关键词： Zero-electron-mass limit Quasi-neutral limit Zero-relaxation-time limit Hydrodynamic models Plasmas Semiconductors

Novel criteria for exponential synchronization of inner time-varying complex networks with coupling delay

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Chinese Physics B 2012年第4期21卷 145-150页

作者：张群娇赵军产 College of mathematics and Computer Science Wuhan Textile UniversityWuhan 430073China laboratoire de mathématiques Appliquées Universitédu HavreLe Havre Cedex76058France

This paper mainly investigates the exponential synchronization of an inner time-varying complex network with coupling delay. Firstly, the synchronization of complex networks is decoupled into the stability of the corresponding dynamical systems. Based on the lyapunov function theory, some sufficient conditions to guarantee its stability with any given convergence rate are derived, thus the synchronization of the networks is achieved. Finally, the results are illustrated by a simple time-varying network model with a coupling delay. All involved numerical simulations verify the correctness of the theoretical analysis.

关键词： exponential synchronization time varying complex network coupling delay