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ATTRACTORS FOR DISCRETIZATION OF GINZBURG-LANDAU-BBM EQUATIONS

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Journal of Computational Mathematics 2001年第2期19卷 195-204页

作者： Mu-rong Jiang bo-ling guo Department of Mathematics Yunnan UniversityKunming 650091China R&D Center for Parallel Software Institute of SoftwareChinese Academy of SciencesBeijing 100080China Institute of Applied Physics and Computational Mathematics Beijing 100088China

Focuses on a study which discreted Ginzburg-Landau-BBM equations with periodic initial boundary value conditions by the finite difference method in spatial direction. Background on the discretization of the equations and the priori estimates; Existence of the attractors for the discrete system; Estimates of the upper bounds of Hausdorff and fractal dimensions for the attractors.

关键词： attractor spatially discreted Ginzburg-Landau-BBM equations Hausdorff and fractal dimensions

The Quasi-reversibility Method to Solve the Cauchy Problems for Parabolic Equations

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Acta Mathematica Sinica,English Series 2013年第8期29卷 1617-1628页

作者： Jing LI bo ling guo School of Mathematics and Computational Science Changsha University of Science and Technology Institute of Applied Physics and Computational Mathematics

In this paper, on the one hand, we take the conventional quasi-reversibility method to obtain the error estimates of approximate solutions of the Cauchy problems for parabolic equations in a sub-domain of QT with strong restrictions to the measured boundary data. On the other hand, weakening the conditions on the measured data, then combining the duality method in optimization with the quasi-reversibility method, we solve the Cauchy problems for parabolic equations in the presence of noisy data. Using this method, we can get the proper regularization parameter ε that we need in the quasi-reversibility method and obtain the convergence rate of approximate solutions as the noise of amplitude δ tends to zero.

关键词： Ⅲ-posed problems parabolic equations Cauchy problems quasi-reversibility

Stability and Instability of Schwarzschild-AdS for the Nonlinear Einstein-Klein-Gordon System

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Acta Mathematicae Applicatae Sinica 2022年第4期38卷 778-812页

作者： Feng-Xia LIU bo-ling guo Institute of Artificial Intelligence Beihang UniversityBeijing 100083China Institute of Applied Physics and Computational Mathematics Beijing 100088China

In this paper,we study the global behavior of solutions to the spherically symmetric(it means that the problem is 2+2 framework)coupled Nonlinear-Einstein-Klein-Gordon(NLEKG)system in the presence of a negative cosmological *** prove the well posedness of the NLEKG system in the Schwarzschild-AdS spacetimes and that the Schwarzschild-AdS spacetimes(the trivial black hole solutions of the EKG system for whichφ=0 identically)are asymptotically *** perturbations of Schwarzschild-AdS initial data again lead to regular black holes,with the metric on the black hole exterior approaching a SchwarzschildAdS *** argument on the black hole exterior,with the redshift effect and weighted Hardy inequalities playing the fundamental role in the *** integrated decay and pointwise decay estimates are obtained.

关键词： nonlinear-Einstein-Klein-Gordon equation schwarzschild-AdS spacetime well-posedness bootstrap

Solutions of Ginzburg-Landau Theory for Atomic Fermi Gases Near the BCS-BEC Crossover

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Acta Mathematicae Applicatae Sinica 2015年第3期31卷 665-676页

作者： Shu-hong CHEN bo-ling guo School of Mathematics and Statistics Minnan Normal University Institute of Applied Physics and Computational Mathematics

We are concerned with a time-dependent Ginzburg-Landau equations come from the superfluid atomic Fermi-gases near the Feshbach resonance from the fermion-boson model. We obtain the global existence and uniqueness of s... 详细信息

关键词： global existence uniqueness time-dependent Ginzburg-Landau theory BCS-BEC crossover

Existence and Stability of Static Solutions of the Landau-Lifshitz Equation with Multi-direct Effective Field

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Acta Mathematica Sinica,English Series 2004年第6期20卷 1135-1152页

作者： bo ling guo Gan Shan YANG Institute of Applied Physics and Computational Mathematics Center for Nonlinear Studies Department of Mathematics Yunnan Nationalities University Graduate School of Chinese Academy of Engineering Physics

We prove the existence of solutions of the static Landau-Lifshitz equation with multi- direct effective field and with Dirichlet boundary condition,and establish the stability of the solution of Landau-Lifshitz equati... 详细信息

关键词： Landau-Lifshitz equation Liapunov stable Multi-direct effective field

Random Attractors of boussinesq Equations with Multiplicative Noise

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Acta Mathematica Sinica,English Series 2009年第3期25卷 481-490页

作者： Yang Rong LI bo ling guo School of Mathematics and Statistics Southwest China University Chongqing 400715 P. R. China Center for Nonlinear Study Institute of Beijing Applied Physics and Computational Mathematics Beijing 100088 P. R. China

We study the random dynamical system （RDS） generated by the Benald flow problem with multiplicative noise and prove the existence of a compact random attractor for such RDS.

关键词： random dynamical systems random attractor boussinesq equation white noise Wiener process

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

Blowing up of Solutions to the Cauchy Problem for the Generalized Zakharov System with Combined Power-Type Nonlinearities

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Acta Mathematica Sinica,English Series 2012年第9期28卷 1917-1936页

作者： Zai Hui GAN bo ling guo Chun Xiao guo College of Mathematics and Software Science Sichuan Normal University Institute of Applied Physics and Computational Mathematics Department of Mathematics China University of Mining and Technology Beijing

This paper deals with blowing up of solutions to the Cauchy problem for a class of general- ized Zakharov system with combined power-type nonlinearities in two and three space dimensions. On the one hand, for co = ＋oo we obtain two finite time blow-up results of solutions to the aforementioned 4 ≤ p 〈 N＋2/N-2 4 system. One is obtained under the condition a ≥ 0 and 1 ＋ 4/N or a 〈 0 and 1 〈 p 〈 1 ＋（N = 2,3）; the other is established under the condition N = 3, 1 〈 p 〈 N=2/N-2 and α（p - 3）〉 0. On the other hand, for co 〈＋∞ and α（p - 3）〉 0, we prove a blow-up result for solutions with negative energy to the Zakharov system under study.

关键词： Generalized Zakharov system blowing up combined power-type nonlinearities Lyapunov function in time

Global Random Attractors for the Stochastic Dissipative Zakharov Equations

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Acta Mathematicae Applicatae Sinica 2014年第2期30卷 289-304页

作者： Yan-feng guo bo-ling guo Dong-long LI College of Science Guangxi University of Science and Technology Institute of Applied Physics and Computational Mathematics

The stochastic dissipative Zakharov equations with white noise are mainly investigated. The global random attractors endowed with usual topology for the stochastic dissipative Zakharov equations are obtained in the sense of usual norm. The method is to transform the stochastic equations into the corresponding partial differential equations with random coefficients by Ornstein-Uhlenbeck process. The crucial compactness of the global random attractors wiil be obtained by decomposition of solutions.

关键词： stochastic dissipative Zakharov equations global random attractors Ornstein-Uhlenbeck process compactness