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Global smooth solution to a coupled Schrodinger system in atomic Bose-Einstein condensates with two-dimensional spaces

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Frontiers of Mathematics in China 2016年第6期11卷 1515-1532页

作者： Boling GUO Qiaoxin LI Institute of Applied Physics and Computational Mathematics Beijing 100088 China China Academy of Aerospace Aerodynamics Beijing 100074 China

We obtain the global smooth solution of a nonlinear SchrSdinger equations in atomic Bose-Einstein condensates with two-dimensional spaces. By using the Galerkin method and a priori estimates, we establish the global e... 详细信息

关键词： Schrodinger equation Galerkin method a priori estimate global smooth solution

On the Weak Solutions to Steady-State Mixed Navier–Stokes/Darcy Model

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Acta Mathematica Sinica,English Series 2023年第5期39卷 939-951页

作者： Yan Ren HOU Dan Dan XUE Yao Lin JIANG School of Mathematics and Statistics Xi'an Jiaotong UniversityXi'an 710049P.R.China College of Mathematics and System Science Xinjiang UniversityWulumuqi 830046P.R.China College of Mathematics and Physics Chengdu University of TechnologyChengdu 610059P.R.China

In this paper,for the mixed Navier–Stokes/Darcy model with Beavers–Joseph–Saffman’s interface condition,we first establish an a priori estimate for possible weak solutions by means of expanding the coupled *** we prove the existence of weak solutions without the small data and/or large viscosity restriction,which is required for the existence of the weak solutions in *** a direct corollary,we also get the global uniqueness of the weak solution.

关键词： Porous media fow Navier-Stokes equations weak solution a priori estimate existence and global uniqueness

GLOBAL BLOWUP AND BLOWUP RATE estimateS OF SOLUTIONS FOR A CLASS OF NONLINEAR NON-LOCAL REACTION-DIFFUSION PROBLEMS

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Acta Mathematica Scientia 2004年第2期24卷 259-264页

作者：刘其林谢春红陈松林 DepartmentofMathematics SoutheastUniversityNanjing210096China

In this paper, the global blowup properties of solutions for a class of nonlinear non-local reaction-diffusion problems are investigated by the methods of the prior estimates. Moreover, the blowup rate estimate of the... 详细信息

关键词： Non-local reaction-diffusion equation blow-up rate a priori estimate

Global attractor for Hirota equation

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Applied Mathematics(A Journal of Chinese Universities) 2008年第1期23卷 57-64页

作者： ZHANG Rui-feng GUO Bo-ling Institute of Appl. Math. College of Math. and Inform. Sci. Henan Univ. Kaifeng 475001 China. Institute of Appl. Phys. and Comput. Math. Beijing 100088 China.

The long time behavior of solution for Hirota equation with zero order dissipation is studied. The global weak attractor for this system in Hper^k is constructed. And then by exact analysis of the energy equation, it ... 详细信息

关键词： Hirota equation a priori estimate global attractor.

H^1 SOLUTIONS FOR A CLASS OF SEMILINEAR PARABOLIC SYSTEMS

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Acta Mathematica Scientia 1997年第1期17卷 91-96页

作者：严国政 Young Scientist Laboratory of Math. Phys. Inst. of Math. Sci. Academia Sinica Wuhan 430071 China

In this paper, we consider the Cauchy problem of a class of semilinear parabolic system. Firstly, we obtain the local existence of solutions of (1.1),(1.2) in H-1(R(1)), and then we prove the global existence of the s... 详细信息

关键词： parabolic system a priori estimate global solution

Analysis of a time-dependent fluid-solid interaction problem above a local rough surface

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Science China Mathematics 2020年第5期63卷 887-906页

作者： Changkun Wei Jiaqing Yang Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China School of Mathematics and Statistics Xi’an Jiaotong UniversityXi’an 710049China

This paper is concerned with the mathematical analysis of a time-dependent fluid-solid interaction problem associated with a bounded elastic body immersed in a homogeneous air or fluid above a local rough surface. We reformulate the unbounded scattering problem into an equivalent initial-boundary value problem defined in a bounded domain by proposing a transparent boundary condition(TBC) on a hemisphere. Analyzing the reduced problem with the Lax-Milgram lemma and the abstract inversion theorem of the Laplace transform,we prove the well-posedness and stability for the reduced problem. Moreover, an a priori estimate is established directly in the time domain for the acoustic wave and elastic displacement by using the energy method.

关键词： well-posedness stability a priori estimate fluid-solid interaction Laplace transform local rough surface

STABILITY OF THE RAREFACTION WAVE FOR THE GENERALIZED KDV-BURGERS EQUATION

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Acta Mathematica Scientia 2002年第3期22卷 319-328页

作者：王治安朱长江 Laboratory of Nonlinear Analysis Department of MathematicsCentral China Normal University Wuhan 430079

This paper is concerned with the stability of the rarefaction wave for the generalized KdV-Burgers equation [GRAPHICS] Roughly speaking, under the assumption that u(-) 0 as t --> infinity, where u(R)(x/t) is the rare... 详细信息

关键词： XdV-Burgers equation rarefaction wave a priori estimate L-2-energy method

Boundary Layer Solution of the Boltzmann Equation for Specular Boundary Condition

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Acta Mathematicae Applicatae Sinica 2023年第1期39卷 65-94页

作者： Fei-min HUANG Zai-hong JIANG Yong WANG Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China Department of Mathematics Zhejiang Normal UniversityJinhua 321004China

In the paper,we establish the existence of steady boundary layer solution of Boltzmann equation with specular boundary condition in Lx,v2∩Lx,v∞in *** uniqueness,continuity and exponential decay of the solution are obtained,and such estimates are important to prove the Hilbert expansion of Boltzmann equation for half-space problem with specular boundary condition.

关键词： Botlzmann equation boundary layer steady problem specular boundary condition a priori estimate

LONG TIME BEHAVIOR FOR SOLUTION OF INITIAL-BOUNDARY VALUE PROBLEM OF ONE CLASS OF SYSTEMS WITH MULTIDIMENSIONAL INHOMOGENEOUS GBBM EQUATIONS

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Applied Mathematics and Mechanics(English Edition) 2005年第6期26卷 716-721页

作者：房少梅郭柏灵 Department of Mathematics Shaoguan University Institute of Applied Physics and Computational Mathematics

The following initial-boundary value problem for the systems with multidimensional inhomogeneous generalized Benjamin-Bona-Mahony ( GBBM ) equations is reviewed. The existence of global attractors of this problem was ... 详细信息

关键词： multidimensional GBBM equation a priori estimate global attractor