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EXISTENCE AND STABILITY OF PERIODIC AND ALMOST PERIODIC SOLUTIONS TO THE BOUSSINESQ SYSTEM IN unbounded domains

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Acta Mathematica Scientia 2022年第5期42卷 1875-1901页

作者： Thieu Huy NGUYEN Truong Xuan PHAM Thi Ngoc Ha VU The Sac LE School of Applied Mathematics and Informatics Hanoi University of Science and Technology Vien Toan ung dung va Tin hocDai hoc Bach khoa Hanoi 1DaiCoVietHanoiVietnam Department of Mathematics Faculty of Information TechnologyThuyloi university Khoa Cong nghe Thong tinBo mon ToanDai hoc Thuy loi175 Tay SonDong DaHa NoiViet Nam Thuyloi University Dai hoc Thuy Loi175 Tay SonDong DaHanoiViet Nam

In this paper we investigate the existence and stability of periodic solutions(on a half-line R_(+))and almost periodic solutions on the whole line time-axis R to the Boussinesq system on several classes of unbounded domains of R^(n) in the framework of interpolation *** the linear Boussinesq system we combine the L^(p)—L^(q)-smoothing estimates and interpolation functors to prove the existence of bounded mild ***,we prove the existence of periodic solutions by invoking Massera’s *** also prove the existence of almost periodic *** we use the results of the linear Boussinesq system to establish the existence,uniqueness and stability of the small periodic and almost periodic solutions to the Boussinesq system using fixed point arguments and interpolation *** results cover and extend the previous ones obtained in[13,34,38].

关键词： Boussinesq systems periodic solutions almost periodic solutions unbounded domains smoothing estimates dual estimates interpolation spaces stability

COMPOSITE LEGENDRE-LAGUERRE APPROXIMATION IN unbounded domains

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Journal of Computational Mathematics 2001年第1期19卷 101-112页

作者： Ben-yu Guo He-ping Ma Department of Mathematics Shanghai Normal UniversityShanghai 200234China Department of Mathematics Shanghai UniversityJiadingShanghai 201800China

Examines the development of the composite legendre approximation in unbounded domains. Proof of the stability and convergence of a proposed scheme; Discussion of two-dimensional exterior problems; Error estimations.

关键词： composite spectral approximation unbounded domains exterior problems

On Some Elliptic Problems in unbounded domains

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Chinese Annals of Mathematics,Series B 2018年第3期39卷 597-606页

作者： Michel CHIPOT Dedicated to Philippe G. Ciarlet on the occasion of his 80th birthda

The author presents a method allowing to obtain existence of a solution for some elliptic problems set in unbounded domains,and shows exponential rate of convergence of the approximate solution toward the solution.

关键词： Elliptic Exponential convergence unbounded domains

Periodic Solutions in unbounded domains for the Boussinesq System

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Acta Mathematica Sinica,English Series 2010年第5期26卷 837-862页

作者： Elder Jesús VILLAMIZAR-ROA María ngeles RODRíGUEZ-BELLIDO Marko Antonio ROJAS-MEDAR Escuela de Matemáticas Universidad Nacional de Colombia Dpto. Ecuaciones Diferenciales y Análisis Numérico Universidad de Sevilla Aptdo Dpto. de Ciencias Básicas Facultad de Ciencias Universidad del Bío BíoCampus Fernando May

Assuming that the external forces of the system are small enough, the reference temperature being a periodic function, we study the existence, the uniqueness and the regularity of time-periodic solutions for the Boussinesq equations in several classes of unbounded domains of Rn. Our analysis is based on the framework of weak-Lp spaces.

关键词： Boussinesq equations strong periodic solutions unbounded domains

Numerical Solution of Blow-Up Problems for NonlinearWave Equations on unbounded domains

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Communications in Computational Physics 2013年第8期14卷 574-598页

作者： Hermann Brunner Hongwei Li Xiaonan Wu Department of Mathematics Hong Kong Baptist UniversityKowloon TongHong Kong Department of Mathematics and Statistics Memorial University of NewfoundlandSt.John’sNLA1C 5S7Canada College of Mathematical Sciences Shandong Normal UniversityJinan250014P.R.China.

The numerical solution of blow-up problems for nonlinear wave equations on unbounded spatial domains is *** the unified approach,which is based on the operator splitting method,we construct the efficient nonlinear local absorbing boundary conditions for the nonlinear wave equation,and reduce the nonlinear problem on the unbounded spatial domain to an initial-boundary-value problem on a bounded *** the finite difference method is used to solve the reduced problem on the bounded computational ***,a broad range of numerical examples are given to demonstrate the effectiveness and accuracy of our method,and some interesting propagation and behaviors of the blow-up problems for nonlinear wave equations are observed.

关键词： Finite-time blow-up nonlinear wave equation absorbing boundary conditions finite differencemethod unbounded domains

Some Properties of Cauchy-type Singular Integral Operator on unbounded domains

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Journal of Mathematical Research with Applications 2014年第5期34卷 575-586页

作者： Liping WANG Yuying QIAO Weiping ZHANG College of Mathematics and Information Science Hebei Normal University

On the basis of introducing the modified Cauchy kernel,we discuss the Holder continuity of the Cauchy-type singular integral operator on unbounded domains for regular functions by dividing into the following three cases:two points are on the boundary of region;one point is on the boundary and another point is in the interior(or exterior) of the region;two points are in the interior(or exterior) of the region.

关键词： regular function Cauchy-type singular integral operator unbounded domains H(o│¨)lder continuity.

ARTIFICIAL BOUNDARY METHOD FOR THE THREE-DIMENSIONAL EXTERIOR PROBLEM OF ELASTICITY

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Journal of Computational Mathematics 2005年第6期23卷 603-618页

作者： Hou-de Han Chun-xiong Zheng Department of Mathematical Sciences Tsinghua University Beijing 100084 China Department of Mathematics University of Science and Technology of China Hefei 230026 China

The exact boundary condition on a spherical artificial boundary is derived for the three-dimensional exterior problem of linear elasticity in this paper. After this boundary condition is imposed on the artificial boundary, a reduced problem only defined in a bounded domain is obtained. A series of approximate problems with increasing accuracy can be derived if one truncates the series term in the variational formulation, which is equivalent to the reduced problem. An error estimate is presented to show how the error depends on the finite element discretization and the accuracy of the approximate problem. In the end, a numerical example is given to demonstrate the performance of the proposed method.

关键词： artificial boundary method unbounded domains elasticity

On the Minimal Solutions of Variational Inequalities in Orlicz-Sobolev Spaces

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Chinese Annals of Mathematics,Series B 2021年第3期42卷 333-356页

作者： Ge DONG Department of Arts and Science Teaching Shanghai University of Medicine and Health SciencesShanghai 201318China

In this paper,the author studies the existence of the minimal nonnegative solutions of some elliptic variational inequalities in Orlicz-Sobolev spaces on bounded or unbounded *** gets some comparison results between different solutions as tools to pass to the limit in the problems and to show the existence of the minimal solutions of the variational inequalities on bounded domains or unbounded *** both cases,coercive and noncoercive operators are *** sufficient and necessary conditions for the existence of the minimal nonnegative solution of the noncoercive variational inequality on bounded domains are established.

关键词： Orlicz-Sobolev spaces Elliptic variational inequalities Minimal nonnegative solutions Bounded domains unbounded domains

FINITE DIFFERENCE METHODS FOR THE HEAT EQUATION WITH A NONLOCAL BOUNDARY CONDITION

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Journal of Computational Mathematics 2015年第1期33卷 17-32页

作者： V. Thomee A.S. Vasudeva Murthy Mathematical Sciences Chalmers University of Technology and University of Gothenburg SE-412 96 GSteborg Sweden TIFR Centre for Appl. Math Yelahanka New Town Bangalore India

We consider the numerical solution by finite difference methods of the heat equation in one space dimension, with a nonlocal integral boundary condition, resulting from the truncation to a finite interval of the problem on a semi-infinite interval. We first analyze the forward Euler method, and then the 0-method for 0 〈 θ ≤ 1, in both cases in maximum-norm, showing O（h2 ＋ k） error bounds, where h is the mesh-width and k the time step. We then give an alternative analysis for the case θ= 1/2, the Crank-Nicolson method, using energy arguments, yielding a O（h2 ＋ k3/2） error bound. Special attention is given the approximation of the boundary integral operator. Our results are illustrated by numerical examples.

关键词： Heat equation Artificial boundary conditions unbounded domains productquadrature.