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Long time behavior for damped generalized coupled nonlinear wave equations. Ⅱ.unbounded domain

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Communications in Nonlinear Science and Numerical Simulation 2001年第2期6卷 107-110页

作者： Shaomei FANG and Boling GUO Department of Mathematics, Shaoguan University, Shaoguan 512005, China Graduate School, China Academy of Engineering Physics, Beijing 100088, China Center for Nonlinear Studies, Institute of Applied Physics and Computational Department of Mathematics Shaoguan University Shaoguan 512005 China Graduate School China Academy of Engineering Physics Beijing 100088 China Center for Nonlinear Studies Institute of Applied Physics and Computational mathematics Beijing 100088 China

In this paper, by using a priori estimates in the weighted space, the existence of the global attractor for the damped generalized coupled nonlinear wave equations in an unbounded domain is obtained.

关键词： unbounded domain weighted space attractor

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EXPONENTIAL ATTRACTORS OF THE GINZBURG-LANDAU-BBM EQUATIONS IN AN unbounded domain

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Acta Mathematicae Applicatae Sinica 2001年第4期17卷 484-493页

作者：戴正德蒋慕蓉 Department of Mathematics Yunnan University Kunming China

In this paper, the existence of the exponential attractors for the Ginzburg-Landau-BBM equations in an unbounded domain is proved by using weighted function and squeezing property.

关键词： Exponential attractor Ginzburg-Landau-BBM equations unbounded domain weighted function squeezing property

ATTRACTORS FOR GENERALIZED GINZBURG-LANDAU-BBM EQUATIONS IN AN unbounded domain

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Acta Mathematicae Applicatae Sinica 2001年第3期17卷 317-325页

作者：蒋慕蓉郭柏灵 Department of Mathematics Yunnan University Kunming China R & D Center for Parallel Software Institute of Software Chinese Academy of Sciences Beijing China Institute of Applied Physics and Computational Mathematics Beijing China

By the interpolation inequality and a priori estimates in the weighted space, the existence of global solutions for generalized Ginzburg-Landau equation coupled with BBM equation in an unbounded domain is considered, ... 详细信息

关键词： unbounded domain weighted space attractor generalized Ginzburg-Landau-BBM equations

ON NONLINEAR HYPERBOLIC EQUATION IN unbounded domain

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Applied Mathematics and Mechanics(English Edition) 1992年第3期13卷 255-261页

作者：耿堤屈长征 Lanzhou University Lanzhou

The following nonlinear hyperbolic equation is discussed in this paper:where A= -? + Iandx∈Rn. The model comes from the transverse deflection equation of an extensible beam. We prove that there exists a unique local ... 详细信息

关键词： nonlinear hyperbolic equations unbounded domain energy estimation fixed point method

Attractors for the Ginzburg-Landau-BBME quations in an unbounded domain

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Communications in Nonlinear Science and Numerical Simulation 1998年第2期 26-30页

作者： Boling GUO * and Murong JIANG , * (Institute of Applied Physics and Computational Mathematics, Beijing, 100088, China) (Department of Mathematics, Yunnan University, Kunming 650091) (Graduate School of China Ac

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关键词： unbounded domain attractor Ginzburg Landau coupled with BBM equation

Asymptotic Behavior for A Class of Non-autonomous Nonclassical Parabolic Equations with Delay on unbounded domain

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Chinese Quarterly Journal of Mathematics 2019年第4期34卷 410-430页

作者： ZHANG Fang-hong BAI Li-hong Regional Circular Economy key Laboratory of Gansu Higher Institutions LanzhouChina Department of Mathematics Longqiao College of Lanzhou University of Finance and EconomicsLanzhouChina Department of Basic Courses Gansu Institute of Architectural TechnologyLanzhouChina

In this article,we investigate the longtime behavior for the following nonautonomous nonclassical parabolic equations on unbounded domain ut−∆ut−∆u+λu=f(x,u(x,t−ρ(t)))+g(x,t).Under some suitable conditions on the delay term f and the non-autonomous forcing term g,we prove the existence of uniform attractors in Banach space CH1(RN)for the multivalued process generated by non-autonomous nonclassical parabolic equations with delays in unbounded domain.

关键词： Uniform attractors Asymptotic behavior Multi-valued process Nonclassical parabolic equations with delay unbounded domain

The Existence of Positive Solution for Singular Boundary Value Problems of First Order Differential Equation on unbounded domains

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Acta Mathematicae Applicatae Sinica 2009年第1期25卷 95-104页

作者： Xing-qiu Zhang Jing-xian Sun Department of Mathematics Liaocheng University Liaocheng Shandong 252059 China Department of Mathematics Xuzhou Normal University Xuzhou Jiangsu 221116 China

By constructing a special cone and using cone compression and expansion fixed point theorem, this paper presents some existence results of positive solutions of singular boundary value problem on unbounded domains for a class of first order differential equation. As applications of the main results, two examples are given at the end of this paper.

关键词： Singular equation unbounded domain positive solution

The existence and concentration of weak solutions to a class of p-Laplacian type problems in unbounded domains

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Science China Mathematics 2014年第9期57卷 1927-1952页

作者： HE Yi LI GongBao School of Mathematics and Statistics Central China Normal University

In this paper,we study the existence and concentration of weak solutions to the p-Laplacian type elliptic problem-εp△pu+V(z)|u|p-2u-f(u)=0 in Ω,u=0 on ■Ω,u>0 in Ω,N>p>2,where Ω is a domain in RN,possibly unbounded,with empty or smooth boundary,εis a small positive parameter,f∈C1(R+,R)is of subcritical and V:RN→R is a locally Hlder continuous function which is bounded from below,away from zero,such that infΛV0 such that for anyε∈(0,ε0],the above mentioned problem possesses a weak solution uεwith exponential ***,uεconcentrates around a minimum point of the potential V inΛ.Our result generalizes a similar result by del Pino and Felmer(1996)for semilinear elliptic equations to the p-Laplacian type problem.

关键词： existence concentration the p-Laplacian type unbounded domain

Efficient Mapping of High Order Basis Sets for unbounded domains

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Communications in Computational Physics 2018年第6期24卷 69-85页

作者： Faisal Mumtaz Fahhad H.Alharbi College of Science and Engineering Hamad Bin Khalifa UniversityDohaQatar Qatar Environment&Energy Research Institute(QEERI) Hamad Bin Khalifa UniversityDohaQatar

Many physical problems involve unbounded domains where the physical quantities vanish at ***,this has been handled using different techniques such as domain truncation,approximations using infinitely extended and vanishing basis sets,and mapping bounded basis sets using some coordinate *** technique has its own advantages and ***,approximating simultaneously and efficiently a wide range of decaying rates has persisted as major ***,coordinate transformation,if not carefully implemented,can result in non-orthogonal mapped basis *** this work,we revisited this issue with an emphasize on designing appropriate transformations using sine series as basis *** transformations maintain both the orthogonality and the ***,using simple basis set(sine function)help avoid the expensive numerical *** the calculations,four types of physically recurring decaying behaviors are considered,which are:non-oscillating and oscillating exponential decays,and non-oscillating and oscillating algebraic *** results and the analyses show that properly designed high-order mapped basis sets can be efficient tools to handle challenging physical problems on unbounded *** rate ranges as large of 6 orders of magnitudes can be approximated efficiently and concurrently.

关键词： Mapped basis sets unbounded domain spectral method