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WEAK-STRONG UNIQUENESS FOR THREE DIMENSIONAL INCOMPRESSIBLE ACTIVE LIQUID CRYSTALS
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作者 Fan YANG Congming LI 《Acta Mathematica Scientia》 SCIE CSCD 2024年第4期1415-1440,共26页
The hydrodynamics of active liquid crystal models has attracted much attention in recent years due to many applications of these models.In this paper,we study the weak-strong uniqueness for the Leray-Hopf type weak so... The hydrodynamics of active liquid crystal models has attracted much attention in recent years due to many applications of these models.In this paper,we study the weak-strong uniqueness for the Leray-Hopf type weak solutions to the incompressible active liquid crystals in R^(3).Our results yield that if there exists a strong solution,then it is unique among the Leray-Hopf type weak solutions associated with the same initial data. 展开更多
关键词 analysis of parabolic and elliptic types weak-strong uniqueness active liquid crystals weak solution energy equality
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Local existence and uniqueness of solutions to the evolutionary model for magnetoviscoelasticity
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作者 YE Ting-ting WANG Guang-wu HUANG Gui-huo 《广州大学学报(自然科学版)》 CAS 2024年第4期77-90,共14页
In this paper,we prove the local existence and uniqueness of solutions to the evolutionary model for magnetoviscoelasticity in R^(2),R^(3).This model consists of an incompressible Navier-Stokes,a regularized system fo... In this paper,we prove the local existence and uniqueness of solutions to the evolutionary model for magnetoviscoelasticity in R^(2),R^(3).This model consists of an incompressible Navier-Stokes,a regularized system for the evolution of the deformation gradient and the Landau-Lifshitz-Gilbert system for the dynamics of the mag-netization.Our approach depends on approximating the system with a sequence of perturbed systems. 展开更多
关键词 the evolutionary model for magnetoviscoelasticity local solution uniqueness perturbed systems
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Strong Uniqueness of Best Approximations from RS-sets in Banach Spaces 被引量:1
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作者 何金苏 李冲 《Journal of Southeast University(English Edition)》 EI CAS 2001年第1期70-72,共3页
The problem of strong uniqueness of best approximation from an RS set in a Banach space is considered. For a fixed RS set G and an element x∈X , we proved that the best approximation g * to x from ... The problem of strong uniqueness of best approximation from an RS set in a Banach space is considered. For a fixed RS set G and an element x∈X , we proved that the best approximation g * to x from G is strongly unique. 展开更多
关键词 best approximation RS set strong uniqueness
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The Global Uniqueness of Solutions for a Class of Inverse Problem in 1-D Wave Equations of Hyperbolic Type 被引量:1
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作者 叶留青 司清亮 《Chinese Quarterly Journal of Mathematics》 CSCD 2002年第3期107-110,共4页
This paper has given the global uniquene ss theory of solutions for a class of inverse problem in 1_D Wave equation of hype rbolic type.
关键词 D Wave equations of hyperbolic inverse proble m global uniqueness
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Uniqueness of the Viscosity Solutions for the Initial Value Problem of One Type of Second Order Partial Differential Equation
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作者 刘长河 郇中丹 童明生 《Journal of Beijing Institute of Technology》 EI CAS 1998年第1期6-11,共6页
Aim To prove the uniqueness of the viscosity solutions for the initial value problems of one type of second order parabolic partial differential equations: Methods Using comparison theorem. Results and Conclusion If u... Aim To prove the uniqueness of the viscosity solutions for the initial value problems of one type of second order parabolic partial differential equations: Methods Using comparison theorem. Results and Conclusion If u0 is uniform continuousfunction in RN , F is continuous function in RNx(N) and F is degenerate elliptic, then thisequation has the sole viscosity solution. 展开更多
关键词 viscosity solution degenerate ellipticity the uniqueness of the solutions
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On existence and uniqueness of the solution of elastoplastic contact problems
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作者 郭小明 《Journal of Southeast University(English Edition)》 EI CAS 2009年第2期232-235,共4页
Contact problems and elastoplastic problems are unified and described by the variational inequality formulation, in which the constraints of the constitutional relations for elastoplastic materials and the contact con... Contact problems and elastoplastic problems are unified and described by the variational inequality formulation, in which the constraints of the constitutional relations for elastoplastic materials and the contact conditions are relaxed totally. First, the coerciveness of the functional is proved. Then the uniqueness of the solution of variational inequality for the elastoplastic contact problems is demonstrated. The existence of the solution is also demonstrated according to the sufficient conditions for the solution of the elliptic variational inequality. A mathematical foundation is developed for the variational extremum principle of elastoplastic contact problems. The developed variational extremum forms can give an effective and strict mathematical modeling to solve contact problems with mathematical programming. 展开更多
关键词 ELASTOPLASTIC contact problem EXISTENCE uniqueness COERCIVENESS variational extremum form
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A Note of the Uniqueness Criterion for Single Birth Processes
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作者 吴群英 《Chinese Quarterly Journal of Mathematics》 CSCD 2002年第3期88-92,共5页
This paper is devoted to studying the si ngle birth processes. The uniqueness criterion for the processes is presented.
关键词 single birth process uniqueness criterion zero _exit REGULAR
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Equivalence of Uniqueness in Law and Joint Uniqueness in Law for SDEs Driven by Poisson Processes
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作者 Huiyan Zhao Chunhua Hu Siyan Xu 《Applied Mathematics》 2016年第8期784-792,共9页
We give an extension result of Watanabe’s characterization for 2-dimensional Poisson processes. By using this result, the equivalence of uniqueness in law and joint uniqueness in law is proved for one-dimensional sto... We give an extension result of Watanabe’s characterization for 2-dimensional Poisson processes. By using this result, the equivalence of uniqueness in law and joint uniqueness in law is proved for one-dimensional stochastic differential equations driven by Poisson processes. After that, we give a simplified Engelbert theorem for the stochastic differential equations of this type. 展开更多
关键词 uniqueness in Law Joint uniqueness in Law Poisson Process Engelbert Theorem
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UNIQUENESS OF ENTIRE FUNCTIONS SHARING ONE VALUE 被引量:6
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作者 林秀清 林伟川 《Acta Mathematica Scientia》 SCIE CSCD 2011年第3期1062-1076,共15页
We deal with the problem of entire functions sharing one value weakly. Moreover, we improve and generalize some former results obtained by J.-F.Chen, et al. [6], Y.Xu and H.L.Qiu [4], M.L. Fang [5], C.C. Yang, and X.H... We deal with the problem of entire functions sharing one value weakly. Moreover, we improve and generalize some former results obtained by J.-F.Chen, et al. [6], Y.Xu and H.L.Qiu [4], M.L. Fang [5], C.C. Yang, and X.H. Hua [3]. 展开更多
关键词 uniqueness entire function shared value meromorphic function
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THE EXISTENCE AND LOCAL UNIQUENESS OF MULTI-PEAK POSITIVE SOLUTIONS TO A CLASS OF KIRCHHOFF EQUATION 被引量:4
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作者 Gongbao LJ Yahui NIU 《Acta Mathematica Scientia》 SCIE CSCD 2020年第1期90-112,共23页
In the present paper,we consider the nonlocal Kirchhoff problem-(ε^2a+εb∫|■u|^2)Δu+u=Q(x)u^p,u>0 in R^3,,where a,b>0,1<p<5 andε>0 is a parameter.Under some assumptions on Q(x),we show the existenc... In the present paper,we consider the nonlocal Kirchhoff problem-(ε^2a+εb∫|■u|^2)Δu+u=Q(x)u^p,u>0 in R^3,,where a,b>0,1<p<5 andε>0 is a parameter.Under some assumptions on Q(x),we show the existence and local uniqueness of positive multi-peak solutions by LyapunovSchmidt reduction method and the local Pohozaev identity method,respectly. 展开更多
关键词 KIRCHHOFF equations multi-peak positive solutions LOCAL uniqueness LOCAL Pohozaev identity Lyapunov-Schmidt reduction
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ON UNIQUENESS OF MEROMORPHIC FUNCTIONS WITH SHARED-SETS IN AN ANGULAR DOMAIN 被引量:4
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作者 陈省江 林伟川 《Acta Mathematica Scientia》 SCIE CSCD 2011年第1期194-206,共13页
In this article, we deal with the uniqueness problems on meromorphic functions sharing two finite sets in an angular domain instead of the whole plane C. In particular, we investigate the uniqueness for meromorphic fu... In this article, we deal with the uniqueness problems on meromorphic functions sharing two finite sets in an angular domain instead of the whole plane C. In particular, we investigate the uniqueness for meromorphic functions of infinite order in an angular domain and obtain some results. Moreover, examples show that the conditions in theorems are necessary. 展开更多
关键词 SHARED-SET uniqueness meromorphic function angular domain infinite order
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Existence and Uniqueness of Solutions for Higher Order Nonlinear Multi-point Boundary Value Problems 被引量:7
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作者 PEI Ming-he Sung-Kag Chang 《Chinese Quarterly Journal of Mathematics》 CSCD 2009年第2期258-266,共9页
In this paper, the existence and uniqueness theorems of solutions of k-point boundary value problems for nth-order nonlinear differential equations are established by Leray-Schauder continuation theorem.
关键词 nth-order nonlinear differential equations k-point boundary value problem EXISTENCE uniqueness
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UNIQUENESS PROBLEM FOR MEROMORPHIC MAPPINGS IN SEVERAL COMPLEX VARIABLES INTO P^N(C) WITH TRUNCATED MULTIPLICITIES 被引量:4
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作者 涂振汉 王中华 《Acta Mathematica Scientia》 SCIE CSCD 2013年第1期122-130,共9页
This paper proves some uniqueness theorems for meromorphic mappings in several complex variables into the complex projective space p^N(C) with truncated multiplicities, and our results improve some earlier work.
关键词 meromorphic mappings truncated multiplicities uniqueness theorems value distribution theory
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Some results on zeros and uniqueness of difference-differential polynomials 被引量:5
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作者 LIU Kai LIU Xin-ling CAO Ting-bin 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2012年第1期94-104,共11页
We consider the zeros distributions of difference-differential polynomials which are the derivatives of difference products of entire functions. We also investigate the uniqueness problems of difference-differential p... We consider the zeros distributions of difference-differential polynomials which are the derivatives of difference products of entire functions. We also investigate the uniqueness problems of difference-differential polynomials of entire functions sharing a common value. 展开更多
关键词 ZERO sharing value uniqueness difference-differential polynomial.
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Uniqueness,reciprocity theorem,and plane waves in thermoelastic diffusion with a fractional order derivative 被引量:4
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作者 Rajneesh Kumar Vandana Gupta 《Chinese Physics B》 SCIE EI CAS CSCD 2013年第7期286-297,共12页
In this work, a theory of thermoelasticity with diffusion is taken into consideration by using the methodology of fractional calculus. The governing equations for particle motion in a homogeneous anisotropic fractiona... In this work, a theory of thermoelasticity with diffusion is taken into consideration by using the methodology of fractional calculus. The governing equations for particle motion in a homogeneous anisotropic fractional order generalized thermoelastic diffusive medium are presented. Uniqueness and reciprocity theorems are proved. The plane wave propagation in the homogeneous transversely isotropic thermoelastic diffusive medium with fractional order derivative is studied. For the two-dimensional problem, there exist a quasi-longitudinal wave, a quasi-transverse wave, a quasi-mass diffusion wave, and a quasi-thermal wave. From the obtained results, the different characteristics of waves, like phase velocity, attenuation coefficient, specific loss, and penetration depth, are computed numerically and presented graphically. Some special cases are also discussed. 展开更多
关键词 thermoelastic diffusion fractional calculus uniqueness theorem reciprocity theorem
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Calibration and uniqueness analysis of microparameters for DEM cohesive granular material 被引量:4
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作者 Songtao Ji Jurij Karlovšek 《International Journal of Mining Science and Technology》 SCIE EI CAS CSCD 2022年第1期121-136,共16页
The differential evolution(DE)algorithm was deployed to calibrate microparameters of the DEM cohesive granular material.4 macroparameters,namely,uniaxial compressive strength,direct tensile strength,Young’s modulus a... The differential evolution(DE)algorithm was deployed to calibrate microparameters of the DEM cohesive granular material.4 macroparameters,namely,uniaxial compressive strength,direct tensile strength,Young’s modulus and Poisson’s ratio,can be calibrated to high accuracy.The best calibration accuracy could reach the sum of relative errors RE_(sum)<0.1%.Most calibrations can be achieved with RE_(sum)<5%within hours or RE_(sum)<1%within 2 days.Based on the calibrated results,microparameters uniqueness analysis was carried out to reveal the correlation between microparameters and the macroscopic mechanical behaviour of material:(1)microparameters effective modulus,tensile strength and normal-to-shear stiffness ratio control the elastic behaviour and stable crack growth,(2)microparameters cohesion and friction angles present a negative linear correlation that controls the axial strain and lateral strain prior to the peak stress,and(3)microparameters friction coefficient controls shear crack friction and slip mainly refers to the unstable crack behaviour.Consideration of more macroparameters to regulate the material mechanical behaviour that is dominated by shear crack and slip motion is highlighted for future study.The DE calibration method is expected to serve as an alternative method to calibrate the DEM cohesive granular material to its peak strength. 展开更多
关键词 Discrete element method(DEM) Particle flow code(PFC) Differential evolution(DE) Parameter calibration uniqueness analysis Post-peak behaviour
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EXISTENCE AND UNIQUENESS FOR THIRD ORDER NONLINEAR BOUNDARY VALUE PROBLEMS 被引量:5
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作者 WANG GUOCAN Department of Basic Science, Dalian Institute of Railway Technology, Dalian 116022 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 1996年第1期7-16,共10页
In this paper, the existence and uniqueness of solutions for boundary valueproblem x′′′=f(t, x, x′, x″), x(0)=A, x′(0)=B, g(x′(1), x″(1))=0 are studied byusing Volterra type operator and upper and lower soluti... In this paper, the existence and uniqueness of solutions for boundary valueproblem x′′′=f(t, x, x′, x″), x(0)=A, x′(0)=B, g(x′(1), x″(1))=0 are studied byusing Volterra type operator and upper and lower solutions. Our results improve someknown works. 展开更多
关键词 Third order nonlinear boundary value problem existence and uniqueness Volterra type operator upper and lower solutions.
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UNIQUENESS PROBLEM WITH TRUNCATED MULTIPLICITIES OF MEROMORPHIC MAPPINGS FOR MOVING TARGETS 被引量:4
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作者 陈志华 李燕华 颜启明 《Acta Mathematica Scientia》 SCIE CSCD 2007年第3期625-634,共10页
In this article, two uniqueness theorems of meromorphic mappings on moving targets with truncated multiplicities are proved.
关键词 Moving targets uniqueness theorem value distribution
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Uniqueness Theorems for Meromorphic Functions of Order Less than One 被引量:14
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作者 李玉华 《Northeastern Mathematical Journal》 CSCD 2000年第4期411-416,共6页
In this paper we study the uniqueness of certain meromorphic functions. It is shown that any two nonconstant meromorphic functions of order less than one, that share four values IM or six values SCM, must be identical... In this paper we study the uniqueness of certain meromorphic functions. It is shown that any two nonconstant meromorphic functions of order less than one, that share four values IM or six values SCM, must be identical. As a consequence, a result due to W. W. Adams and E. G. Straus is generalized. 展开更多
关键词 meromorphic function IM sharing value uniqueness
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UNIQUENESS OF STATIONARY SOLUTIONS WITH VACUUM OF EULER-POISSON EQUATIONS 被引量:3
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作者 邓引斌 郭玉劲 《Acta Mathematica Scientia》 SCIE CSCD 2003年第3期405-412,共8页
In this paper, the uniqueness of stationary solutions with vacuum of Euler-Poisson equations is considered. Through a nonlinear transformation which is a function of density and entropy, the corresponding problem can ... In this paper, the uniqueness of stationary solutions with vacuum of Euler-Poisson equations is considered. Through a nonlinear transformation which is a function of density and entropy, the corresponding problem can be reduced to a semilinear elliptic equation with a nonlinear source term consisting of a power function, for which the classical theory of the elliptic equations leads the authors to the uniqueness result under some assumptions on the entropy function S(x). As an example, the authors get the uniqueness of stationary solutions with vacuum of Euler-Poisson equations for S(x) =|x|θandθ∈{0}∪[2(N-2),+∞). 展开更多
关键词 uniqueness stationary solution Euler-Poisson equation
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