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A NURBS-based, perfectly matched layer method for transient elastodynamics in unbounded domains 认领 引用
1
作者 Arturo Méndez Salas Myung-Jin Choi Sven Klinkel 《Earthquake Engineering and Engineering Vibration》 SCIE EI CSCD 2025年第3期723-742,共20页
In this study,the wave motion in elastodynamics for unbounded media is modeled using an unsplit-field perfectly matched layer(PML)formulation that is solved by employing an isogeometric analysis(IGA).In the adopted co... In this study,the wave motion in elastodynamics for unbounded media is modeled using an unsplit-field perfectly matched layer(PML)formulation that is solved by employing an isogeometric analysis(IGA).In the adopted combination,the non-uniform rational B-spline(NURBS)functions are employed as basis functions.Moreover,the unbounded and artificial domains,defined in the PML method,are contained in a single patch domain.Based on the proposed scheme,the approximation of the geometry problem is set in a new scheme in which the PML’s absorbing and attenuation properties and the description of traveling waves can be represented.This includes a higher continuity and smoother approximation of the computed domain.As high-order NURBS basis functions are non-interpolatory,a penalty method is present to apply a time-dependent displacement load.The performance of the NURBS-based PML is analyzed through numerical examples for 1D and 2D domains,considering homogeneous and heterogeneous media.Further,we verify the long-time numerical stability of the present method.The developed method can be used to simulate hypothetical stratified domains commonly encountered in soil-structure interaction analyses. 展开更多
关键词 perfectly matched layer NURBS elastodynamics unbounded domains transient analysis
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Toeplitz Operators with Unbounded Symbols on Segal-Bargmann Space 认领 引用 被引量：2
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作者 Li HE Guangfu CAO 《Journal of Mathematical Research with Applications》 CSCD 2015年第3期237-255,共19页
In this paper, we construct a function φ in L^2（C^n,dVα） which is unbounded on any neighborhood of each point in C^n such that Tφ is a trace class operator on the Segal- Bargmann space H^2（Cn, dVα）. In additio... In this paper, we construct a function φ in L^2（C^n,dVα） which is unbounded on any neighborhood of each point in C^n such that Tφ is a trace class operator on the Segal- Bargmann space H^2（Cn, dVα）. In addition, we also characterize the Schatten p-class Toeplitz operators with positive measure symbols on H^2 （C^n, dVα）. 展开更多
关键词 Segal-Bargmann space Toeplitz operator unbounded function Schatten class
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ATTRACTORS FOR THE GINZBURG-LANDAU-BBM EQUATIONS IN AN UNBOUNDED DOMAIN 认领 引用 被引量：1
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作者 郭柏灵 蒋慕蓉 《Acta Mathematica Scientia》 SCIE 2000年第1期122-130,共9页
By the interpolating inequality and a priori estimates in the weighted space,the existence of the global solutions for the Ginzburg-Landau equation coupled with the BBM equation in an unbounded domain is considered, a... By the interpolating inequality and a priori estimates in the weighted space,the existence of the global solutions for the Ginzburg-Landau equation coupled with the BBM equation in an unbounded domain is considered, and the existence of the maximal attractor is obtained. 展开更多
关键词 Unbounded domain weighted space attractor Ginzburg-Landau-BBM equations
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ON SOLUTIONS OF BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS WITH JUMPS,WITH UNBOUNDED STOPPING TIMES AS TERMINAL AND WITH NON-LIPSCHITZ COEFFICIENTS,AND PROBABILISTIC INTERPRETATION OF QUASI-LINEAR ELLIPTIC TYPE INTEGRO-DIFFERENTIAL EQUATIO 认领 引用 被引量：1
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作者 司徒荣 王越平 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2000年第6期659-672,共14页
The existence and uniqueness of solutions to backward stochastic differential equations with jumps and with unbounded stopping time as terminal under the non_Lipschitz condition are obtained. The convergence of soluti... The existence and uniqueness of solutions to backward stochastic differential equations with jumps and with unbounded stopping time as terminal under the non_Lipschitz condition are obtained. The convergence of solutions and the continuous dependence of solutions on parameters are also derived. Then the probabilistic interpretation of solutions to some kinds of quasi_linear elliptic type integro_differential equations is obtained. 展开更多
关键词 backward stochastic differential equations(BSDEs) with jumps unbounded stopping time adapted solutions convergence of solutions quasi_linear elliptic equations integro_differential operators.
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INFINITE ELEMENT METHOD FOR PROBLEMS ON UNBOUNDED AND MULTIPLY CONNECTED DOMAINS 认领 引用 被引量：1
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作者 应隆安 《Acta Mathematica Scientia》 SCIE 2001年第4期440-452,共13页
The author studies the infinite element method for the boundary value problems of second order elliptic equations on unbounded and multiply connected domains. The author makes a partition of the domain into infinite n... The author studies the infinite element method for the boundary value problems of second order elliptic equations on unbounded and multiply connected domains. The author makes a partition of the domain into infinite number of elements. Without dividing the domain, as usual, into a bounded one and an exterior one, he derives an initial value problem of an ordinary differential equation for the combined stiffness matrix, then obtains the approximate solution with a small amount of computer work. Numerical examples are given. 展开更多
关键词 finite element method infinite element method unbounded domain multiply connected domain
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PROBABILITY INEQUALITIES FOR SUMS OF INDEPENDENT UNBOUNDED RANDOM VARIABLES 认领 引用
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作者 ZHANG Dixin +1 位作者 WANG Zhicheng 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2001年第5期597-601,共5页
The tail probability inequalities for the sum of independent unbounded random variables on a probability space (Omega, T, P) were studied and a new method was proposed to treat the sum of independent unbounded random ... The tail probability inequalities for the sum of independent unbounded random variables on a probability space (Omega, T, P) were studied and a new method was proposed to treat the sum of independent unbounded random variables by truncating the original probability space (Omega, T, P). The probability exponential inequalities for sums of the results, some independent unbounded random variables were given. As applications of interesting examples were given. The examples show that the method proposed in the paper and the results of the paper are quite useful in the study of the large sample properties of the sums of independent unbounded random variables. 展开更多
关键词 probability exponential inequality unbounded random variables convergence
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A Continuation Method for Solving Fixed Point Problems in Unbounded Convex Sets 认领 引用
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作者 Su MENG-LONG LU XIAN-RUI MA YONG 《Communications in Mathematical Research》 2009年第2期137-142,共6页
In this paper, an unbounded condition is presented, under which we are able to utilize the interior point homotopy method to solve the Brouwer fixed point problem on unbounded sets. Two numerical examples in R3 are pr... In this paper, an unbounded condition is presented, under which we are able to utilize the interior point homotopy method to solve the Brouwer fixed point problem on unbounded sets. Two numerical examples in R3 are presented to illustrate the results in this paper. 展开更多
关键词 unbounded condition interior point homotopy method Brouwer fixed point problem
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NON-EXISTENCE FOR QUASILINEAR ELLIPTIC EQUATIONS IN UNBOUNDED DOMAINS 认领 引用
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作者 沈尧天 马汝念 《Acta Mathematica Scientia》 SCIE 1992年第1期62-70,共9页
Since [1] established the Pohozaev identity in bounded domains, this identity has been the principal tool to deal with the non-existence of the equation
关键词 NON-EXISTENCE FOR QUASILINEAR ELLIPTIC EQUATIONS IN UNBOUNDED DOMAINS ID
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PoincaréProblem for Nonlinear Elliptic Equations of Second Order in Unbounded Domains 认领 引用
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作者 Guochun Wen 《Advances in Pure Mathematics》 2013年第1期172-177,共6页
In [1], I. N. Vekua propose the Poincaré problem for some second order elliptic equations, but it can not be solved. In [2], the authors discussed the boundary value problem for nonlinear elliptic equations of se... In [1], I. N. Vekua propose the Poincaré problem for some second order elliptic equations, but it can not be solved. In [2], the authors discussed the boundary value problem for nonlinear elliptic equations of second order in some bounded domains. In this article, the Poincaré boundary value problem for general nonlinear elliptic equations of second order in unbounded multiply connected domains have been completely investigated. We first provide the formulation of the above boundary value problem and corresponding modified well posed-ness. Next we obtain the representation theorem and a priori estimates of solutions for the modified problem. Finally by the above estimates of solutions and the Schauder fixed-point theorem, the solvability results of the above Poincaré problem for the nonlinear elliptic equations of second order can be obtained. The above problem possesses many applications in mechanics and physics and so on. 展开更多
关键词 Poincaré Boundary Value Problem Nonlinear Elliptic Equations Unbounded Domains
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On the Growth of Transcendental Entire Functions with Unbounded Fatou Components 认领 引用 被引量：1
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作者 伍家凤 徐光伟 王小灵 《Journal of Donghua University(English Edition)》 EI CAS 2006年第2期80-82,共3页
Suppose that f（ z ） is a transcendental entire function and that F（f） contains unbounded Fatou components. In this article, we obtained some links between the lowor bounds of the lower order of f and the angle of ... Suppose that f（ z ） is a transcendental entire function and that F（f） contains unbounded Fatou components. In this article, we obtained some links between the lowor bounds of the lower order of f and the angle of an angular sector which is completely contained in an unbounded Fatou component of F（f）. Then, we investigate the bounded components for the Julia set J（f） of a transcendental entire function f（z ） and obtain a sufficient and necessary condition. 展开更多
关键词 Unbounded Fatou component lower order Fatou sets.
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EXISTENCE AND STABILITY OF PERIODIC AND ALMOST PERIODIC SOLUTIONS TO THE BOUSSINESQ SYSTEM IN UNBOUNDED DOMAINS 认领 引用
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作者 Thieu Huy NGUYEN Truong Xuan PHAM +1 位作者 Thi Ngoc Ha VU The Sac LE 《Acta Mathematica Scientia》 SCIE CSCD 2022年第5期1875-1901,共27页
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 ... 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 Rn in the framework of interpolation spaces.For the linear Boussinesq system we combine the Lp—Lq-smoothing estimates and interpolation functors to prove the existence of bounded mild solutions.Then,we prove the existence of periodic solutions by invoking Massera’s principle.We also prove the existence of almost periodic solutions.Then 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 spaces.Our results cover and extend the previous ones obtained in[13,34,38]. 展开更多
关键词 Boussinesq systems periodic solutions almost periodic solutions unbounded domains smoothing estimates dual estimates interpolation spaces stability
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Random Attractors for Stochastic Reaction-Diffusion Equations with Distribution Derivatives on Unbounded Domains 认领 引用 被引量：3
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作者 Eshag Mohamed Ahmed Ali Dafallah Abdelmajid +1 位作者 Ling Xu Qiaozhen Ma 《Applied Mathematics》 2015年第10期1790-1807,共18页
In this paper, we prove the existence of random attractors for a stochastic reaction-diffusion equation with distribution derivatives on unbounded domains. The nonlinearity is dissipative for large values of the state... In this paper, we prove the existence of random attractors for a stochastic reaction-diffusion equation with distribution derivatives on unbounded domains. The nonlinearity is dissipative for large values of the state and the stochastic nature of the equation appears spatially distributed temporal white noise. The stochastic reaction-diffusion equation is recast as a continuous random dynamical system and asymptotic compactness for this demonstrated by using uniform estimates far-field values of solutions. The results are new and appear to be optimal. 展开更多
关键词 Stochastic Reaction-Diffusion Equation Random Attractors Distribution Derivatives Asymptotic Compactness Unbounded Domain
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Equivalence Relation between Initial Values and Solutions for Evolution p-Laplacian Equation in Unbounded Space 认领 引用
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作者 Liangwei Wang Jingxue Yin Langhao Zhou 《Communications in Mathematical Research》 CSCD 2020年第1期51-67,共17页
In this paper,an equivalence relation between the ω-limit set of initial values and the ω-limit set of solutions is established for the Cauchy problem of evolution p-Laplacian equation in the unbounded space Yσ(RN)... In this paper,an equivalence relation between the ω-limit set of initial values and the ω-limit set of solutions is established for the Cauchy problem of evolution p-Laplacian equation in the unbounded space Yσ(RN).To overcome the difficulties caused by the nonlinearity of the equation and the unbounded solutions,we establish the propagation estimate and the growth estimate for the solutions.It will be demonstrated that the equivalence relation can be used to study the asymptotic behavior of solutions. 展开更多
关键词 Asymptotic behavior evolution p-Laplacian equation unbounded function propagation estimate growth estimate
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THE EXISTENCE OF INFINITELY MANY SO UTIONS OF QUASILINEAR PARTIAL DIFFERENTIAL EQUATIONS IN UNBOUNDED DOMAINS 认领 引用 被引量：1
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作者 李工宝 《Acta Mathematica Scientia》 SCIE 1989年第2期175-188,共14页
In this paper, we use the concentration-compactness principle together with the Mountain Pass Lemma to get the existence of nontrivial solutions and the existence of infinitely many solutions of the problem need not b... In this paper, we use the concentration-compactness principle together with the Mountain Pass Lemma to get the existence of nontrivial solutions and the existence of infinitely many solutions of the problem need not be compact operators from E to R~1. 展开更多
关键词 THE EXISTENCE OF INFINITELY MANY SO UTIONS OF QUASILINEAR PARTIAL DIFFERENTIAL EQUATIONS IN UNBOUNDED DOMAINS
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NORM SUMMABILITY OF NRLUND LOGARITHMIC MEANS ON UNBOUNDED VILENKIN GROUPS 认领 引用
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作者 I. Blahota G. Gàt 《Analysis in Theory and Applications》 2008年第1期1-17,共17页
The （Noerlund） logarithmic means of the Fourier series is：tnf=1/ln ^n-1∑k=1 Skf-k, where ln=^n-1∑k=1 1/k In general, the Fej6r （C, 1） means have better properties than the logarithmic ones. We compare them and ... The （Noerlund） logarithmic means of the Fourier series is：tnf=1/ln ^n-1∑k=1 Skf-k, where ln=^n-1∑k=1 1/k In general, the Fej6r （C, 1） means have better properties than the logarithmic ones. We compare them and show that in the case of some unbounded Vilenkin systems the situation changes. 展开更多
关键词 unbounded Vilenkin group Fejer means logarithmic means norm convergence
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ON NONLINEAR HYPERBOLIC EQUATION IN UNBOUNDED DOMAIN 认领 引用
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作者 耿堤 屈长征 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1992年第3期255-261,共7页
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 ... 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 solution of the above equation as M depends on x. 展开更多
关键词 nonlinear hyperbolic equations unbounded domain energy estimation fixed point method
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Some Properties of Cauchy-type Singular Integral Operator on Unbounded Domains 认领 引用
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作者 Liping WANG Yuying QIAO Weiping ZHANG 《Journal of Mathematical Research with Applications》 CSCD 2014年第5期575-586,共12页
On the basis of introducing the modified Cauchy kernel, we discuss the Hoelder continuity of the Cauchy-type singular integral operator on unbounded domains for regular functions by dividing into the following three c... On the basis of introducing the modified Cauchy kernel, we discuss the Hoelder 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. 展开更多
关键词 regular function Cauchy-type singular integral operator unbounded domains Hoelder continuity.
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Containment control of heterogeneous multi-agent systems subject to Markovian randomly switching topologies and unbounded delays 认领 引用
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作者 Haihua Guo Gang Feng Cong Bi 《Journal of Automation and Intelligence》 2024年第3期152-159,共8页
This paper addresses the problem of containment control for heterogeneous multi-agent systems subject to Markovian randomly switching topologies and unbounded communication delays.The objective is to design a distribu... This paper addresses the problem of containment control for heterogeneous multi-agent systems subject to Markovian randomly switching topologies and unbounded communication delays.The objective is to design a distributed control strategy that ensures the output of each follower converges to the convex hull formed by the outputs of a group of leaders in mean square sense.A novel distributed observer is proposed by tackling both Markovian randomly switching topologies and unbounded delays.Then,a distributed state feedback controller and a distributed output feedback controller are developed based on the distributed observer,respectively.Finally,simulation results are provided to demonstrate the effectiveness of the proposed controllers. 展开更多
关键词 Containment control Markovian randomly switching topologies Unbounded delaysLyapunov method Multi-agent systems
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THE EXPONENTIAL PROPERTY OF SOLUTIONS BOUNDED FROM BELOW TO DEGENERATE EQUATIONS IN UNBOUNDED DOMAINS 认领 引用
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作者 Lidan WANG 《Acta Mathematica Scientia》 SCIE CSCD 2022年第1期323-348,共26页
This paper is focused on studying the structure of solutions bounded from below to degenerate elliptic equations with Neumann and Dirichlet boundary conditions in unbounded domains.After establishing the weak maximum ... This paper is focused on studying the structure of solutions bounded from below to degenerate elliptic equations with Neumann and Dirichlet boundary conditions in unbounded domains.After establishing the weak maximum principles,the global boundary Holder estimates and the boundary Harnack inequalities of the equations,we show that all solutions bounded from below are linear combinations of two special solutions(exponential growth at one end and exponential decay at the other)with a bounded solution to the degenerate equations. 展开更多
关键词 degenerate elliptic equations unbounded domains boundary Harnack inequalities
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BOUNDARY VALUE PROBLEMS FOR FULLY NONLINEAR UNIFORMLY ELLIPTIC EQUATIONS OF SECOND IN UNBOUNDED DOMAINS 认领 引用
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作者 陈德昌 《四川师范大学学报（自然科学版）》 CAS 1991年第1期1-2,共2页
We consider fully nonlinear equations of the formF（z,u,Du,D2u） = F（x,y,u,uz,uy,uzz,uzy,uyy） = 0 （1）in unbounded open subset G = R2\Ωof the plane R2,where F is a real continuous function on U = G×R×R2&... We consider fully nonlinear equations of the formF（z,u,Du,D2u） = F（x,y,u,uz,uy,uzz,uzy,uyy） = 0 （1）in unbounded open subset G = R2\Ωof the plane R2,where F is a real continuous function on U = G×R×R2×R3 and Ω= Ωi,Ωi is a simply connected region （i=1,2,"",N） . We assume the function F hascontinuous partial der ivatives Fuzz, Fuzy, Fuyy. on U.For a real function r C（ G） a real function u（x,y） is called a solution of （1） satisfyingu = r on G,（2）if there exists a constant P0】2 such that u C1 （ ） W2.pLoc0 （G） satisfies （1） almost everywhere and （2）in the common sense.The method for treating the above exterior Dirichlet problem in a given unbounded region is as fol- 展开更多
关键词 Dirichlet unbounded connected subset everywhere exterior infinity assume treating simply
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