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limit behavior OF GROUND STATES OF 2D BINARY BECS IN STEEP POTENTIAL WELLS

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Acta Mathematica Scientia 2023年第1期43卷 409-438页

作者：孔予禛崔志远赵敦 School of Mathematics and Statistics Lanzhou UniversityLanzhou730000China College of Medical Informatics Chongqing Medical UniversityChongqing400016China

We study the ground states of attractive binary Bose-Einstein condensates with N particles,which are trapped in the steep potential wellsλV(x)inℝ*** show that there exists a positive number N*such that if N>N*,the system admits no ground state for anyλ>***,there exist two positive numbers,M*andλ*(N),such that if Nλ*(N),the system admits at least one ground ***λ→∞,for any fixed Nlimit behavior of both positive and semi-trivial ground states.

关键词： ground state binary Bose-Einstein condensate steep potential well limit behavior

On the limit behavior of the magnetic Zakharov system

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Science China Mathematics 2012年第3期55卷 509-540页

作者： HAN LiJia ZHANG JingJun GAN ZaiHui GUO BoLing Department of Mathematics and Physics North China Electric Power University Beijing 102206 China College of Mathematics Physics and Information Engineering Jiaxing University Jiaxing 314001 China College of Mathematics and Software Science Sichuan Normal University Chengdu 610068 China Institute of Applied Physics and Computational Mathematics Beijing 100088 China

In this paper,we prove that the solutions of magnetic Zakharov system converge to those of generalized Zakharov system in Sobolev space H s,s > 3/2,when parameter β→∞.Further,when parameter (α,β) →∞ together,we prove that the solutions of magnetic Zakharov system converge to those of Schro¨dinger equation with magnetic effect in Sobolev space H s,s > 3/***,the convergence rate is also obtained.

关键词： magnetic Zakharov system Zakharov system Schrodinger equation with magnetic effect Cauchyproblem limit behavior

limit behaviors of extended Kalman filter as a parameter estimator for a sinusoidal signal

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Control Theory and Technology 2018年第3期16卷 203-211页

作者： Li XIE State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources School of Control and Computer Engineering North China Electric Power University Beijing 102206 China

In this note, the basic limit behaviors of the solution to Riccati equation in the extended Kalman filter as a parameter estimator for a sinusoidal signal are analytically investigated by using lira sup and lim inf in... 详细信息

关键词： Extended Kalman filter parameter estimator sinusoidal signal covariance matrix limit behavior

THE NEAR-CRITICAL AND SUPER-CRITICAL ASYMPTOTIC behavior IN THE THERMODYNAMIC limit OF REVERSIBLE RANDOM POLYMERIZATION PROCESSES

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Acta Mathematica Scientia 2000年第3期20卷 380-389页

作者：韩东 Department of Mathematics University of Xinjiang Urumqi 830046 China

In this paper, the near-critical and super-critical asymptotic behavior of a reversible Markov process as a chemical model for polymerization was studied. The results of the present paper, together with an analysis of the sub-critical stage, establish the existence of three distinct stages (sub-critical, near-critical and super-critical stages) of polymerization (in the thermodynamic limit as N --> +infinity,),depending on the value of strength of the fragmentation reaction. These three stages correspond to the size of the largest length of polymers of size N to be itself of order log N, Nm/m+1 (m greater than or equal to 2, m not equal 4n, n greater than or equal to 1) and N, respectively.

关键词： polymerization Markov process limit behavior stationary distribution

Analysis of the Boundary Stability of a Diffusion-Reaction System on a Nanolayer

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Journal of Applied Mathematics and Physics 2024年第5期12卷 1682-1698页

作者： Tarik Boulahrouz Mohammed Filali Jamal Messaho Najib Tsouli Laboratory of Applied Mathematics of the Oriental Faculty of Sciences of Oujda Mohamed First University Oujda Morocco

In this paper, the focus is on the boundary stability of a nanolayer in diffusion-reaction systems, taking into account a nonlinear boundary control condition. The authors focus on demonstrating the boundary stability of a nanolayer using the Lyapunov function approach, while making certain regularity assumptions and imposing appropriate control conditions. In addition, the stability analysis is extended to more complex systems by studying the limit problem with interface conditions using the epi-convergence approach. The results obtained in this article are then tested numerically to validate the theoretical conclusions.

关键词： limit behavior limit Problems Feedback Control Epi-Convergence Method Lyapunov Method Nanolayer

A NONLOCAL NONLINEAR BOUNDARYVALUE PROBLEM FOR THE HEAT EQUATIONS

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Chinese Annals of Mathematics,Series B 1996年第3期17卷 365-374页

作者： YAN JINHAI(Department of Mathematics, Fudan University, Shanghai 200433, China) Department of Mathematics Fudan University Shanghai 200433 China

The existence and limit behaviour of the solution for a kind of nonlocal nonlinear boundaryvalue condition on a part of the boundary is studied for the heat equation, which physicallymeans that the potential is the function of the total flux. When this part of boundary shrinksto a point in a certain wayt this condition either results in a Dirac measure or simply disappearsin the corresponding problem.

关键词： Heat equation Nonlinear boundary problem Potential limit behavior

The Cauchy Problem for the Generalized Korteweg-de Vries-Benjamin-Ono Equation with Low Regularity Data

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Acta Mathematica Sinica,English Series 2005年第5期21卷 1191-1196页

作者： Zhao Hui HUO Bo Ling GUO Department of Mathematics School of Sciences Beijing University of Aeronautics and Astronautics Beijing 100083 P. R. China Institute of Applied Physics and Computational Mathematics P. O. Box 8009 Beijing 100088 P. R. China

The Cauchy problem of the generalized Korteweg-de Vries-Benjamin-Ono equation is considered, and low regularity and limit behavior of the solutions are obtained. For k = 1, local well- posedness is obtained for data in H^s（R）（s 〉 -3/4）. For k = 2, local result for data in H^S（R）（s 〉1/4） is obtained. For k = 3, local result for data in H^S（R）（s 〉 -1/6） is obtained. Moreover, the solutions of generalized Korteweg-de Vries-Benjamin-Ono equation converge to the solutions of KdV equation if the term of Benjamin-Ono equation tends to zero.

关键词： Generalized Korteweg-de Vries-Benjamin-Ono equation The Fourier restriction norm,Low regularity solution limit behavior