In this paper,we present a smoothing Newton-like method for solving nonlinear systems of equalities and inequalities.By using the so-called max function,we transfer the inequalities into a system of semismooth equalit...In this paper,we present a smoothing Newton-like method for solving nonlinear systems of equalities and inequalities.By using the so-called max function,we transfer the inequalities into a system of semismooth equalities.Then a smoothing Newton-like method is proposed for solving the reformulated system,which only needs to solve one system of linear equations and to perform one line search at each iteration. The global and local quadratic convergence are studied under appropriate assumptions. Numerical examples show that the new approach is effective.展开更多
In the present paper, we investigate the well-posedness of the global solutionfor the Cauchy problem of generalized long-short wave equations. Applying Kato＇s methodfor abstract quasi-linear evolution equations and a...In the present paper, we investigate the well-posedness of the global solutionfor the Cauchy problem of generalized long-short wave equations. Applying Kato＇s methodfor abstract quasi-linear evolution equations and a priori estimates of solution,we get theexistence of globally smooth solution.展开更多
This paper studies the long time behavior of solutions to the Navier-Stokes equations with linear damping on R^2. The authors prove the existence of L^2-global attractor and Hi-global attractor by showing that the cor...This paper studies the long time behavior of solutions to the Navier-Stokes equations with linear damping on R^2. The authors prove the existence of L^2-global attractor and Hi-global attractor by showing that the corresponding semigroup is asymptotically compact. Thereafter, they establish that the two attractors are the same and thus reveal the asymptotic smoothing effect of the solutions.展开更多
0102258基于卷积的快速分形图像编码[刊]/王冬梅//仪器仪表学报.—2000,21(5).—446～448(E)Y2000-62443-4106 0102259泊松观察的通用平滑方程=A general smoothing equa-tion for poisson observations[会,英]/Malcolm,w.P.＆ Elliott,...0102258基于卷积的快速分形图像编码[刊]/王冬梅//仪器仪表学报.—2000,21(5).—446～448(E)Y2000-62443-4106 0102259泊松观察的通用平滑方程=A general smoothing equa-tion for poisson observations[会,英]/Malcolm,w.P.＆ Elliott,R.J.//1999 IEEE Decision and Control,Vol.4.～4106-4110(HC)展开更多
We consider a class of mathematical programs governed by parameterized quasi-variational inequalities(QVI).The necessary optimality conditions for the optimization problem with QVI constraints are reformulated as a sy...We consider a class of mathematical programs governed by parameterized quasi-variational inequalities(QVI).The necessary optimality conditions for the optimization problem with QVI constraints are reformulated as a system of nonsmooth equations under the linear independence constraint qualification and the strict slackness condition.A set of second order sufficient conditions for the mathematical program with parameterized QVI constraints are proposed,which are demonstrated to be sufficient for the second order growth condition.The strongly BD-regularity for the nonsmooth system of equations at a solution point is demonstrated under the second order sufficient conditions.The smoothing Newton method in Qi-Sun-Zhou [2000] is employed to solve this nonsmooth system and the quadratic convergence is guaranteed by the strongly BD-regularity.Numerical experiments are reported to show that the smoothing Newton method is very effective for solving this class of optimization problems.展开更多
We propose a smoothing trust region filter algorithm for nonsmooth nonconvex least squares problems. We present convergence theorems of the proposed algorithm to a Clarke stationary point or a global minimizer of the ...We propose a smoothing trust region filter algorithm for nonsmooth nonconvex least squares problems. We present convergence theorems of the proposed algorithm to a Clarke stationary point or a global minimizer of the objective function under certain conditions. Preliminary numerical experiments show the efficiency of the proposed algorithm for finding zeros of a system of polynomial equations with high degrees on the sphere and solving differential variational inequalities.展开更多
This paper is intended as an attempt to set up the global smoothing for the periodic Benjamin equation. It is shown that for Hs（T） initial data with 8 〉 -1/2 and for any s 〈 s1〈 min{s ＋ 1,3s ＋ 1}, the differenc...This paper is intended as an attempt to set up the global smoothing for the periodic Benjamin equation. It is shown that for Hs（T） initial data with 8 〉 -1/2 and for any s 〈 s1〈 min{s ＋ 1,3s ＋ 1}, the difference of the evolution with the linear evolution is in Hs1 （T） for all times, with at most polynomial growing HS1 norm. Unlike Korteweg-de Vries （KdV） equation, there are less symmetries of the Benjamin system, especially for the resonant function. The new ingredient is that we need to deal with some new difficulties that are caused by the lack of symmetries.展开更多
In this paper,we prove a general existence theorem of Khler-Einstein metrics on complete Khler manifolds.We use the heat equation method smoothing certain positive (1,1) current in the canonical class.
The smoothness of the solutions to the full Landau equation for Fermi-Dirac particles is investigated.It is shown that the classical solutions near equilibrium to the Landau-Fermi-Dirac equation have a regularizing ef...The smoothness of the solutions to the full Landau equation for Fermi-Dirac particles is investigated.It is shown that the classical solutions near equilibrium to the Landau-Fermi-Dirac equation have a regularizing effects in all variables (time,space and velocity),that is,they become immediately smooth with respect to all variables.展开更多
Let T^2 be a flat two-dimensional torus with fundamental cell domain [-1/2,1/2]×[-1/2,1/2],h（x） a positive smooth function satisfying the symmetric property （8） on T^2.In this paper we give some sufficient co...Let T^2 be a flat two-dimensional torus with fundamental cell domain [-1/2,1/2]×[-1/2,1/2],h（x） a positive smooth function satisfying the symmetric property （8） on T^2.In this paper we give some sufficient condition under which the mean field equation △u = 16π - 16πe^u, has a smooth solution.展开更多
Consider the motion of immersed hypersurfaces driven by surface diffusion flow and give anlower bound on the life span of a smooth immersed solution, which depends only on how muchthe curvature of the initial surface ...Consider the motion of immersed hypersurfaces driven by surface diffusion flow and give anlower bound on the life span of a smooth immersed solution, which depends only on how muchthe curvature of the initial surface is concentrated in space.展开更多
It is known that free-surface flows with small slopes can be described by classical lubrication theory.By replacing the assumption of quasi-parallel flows with local wedge flows,the classical lubrication theory has be...It is known that free-surface flows with small slopes can be described by classical lubrication theory.By replacing the assumption of quasi-parallel flows with local wedge flows,the classical lubrication theory has been generalized to the situation with finite surface slopes and vanishing fluxes,e.g.,steady capillary flows with moving contact lines.In this work,this theory is further extended by imposing the contribution of finite fluxes,which can be modeled by a source/sink flow in a wedge.The resulting lubrication equation is used to investigate the surface morphologies observed in dip coating of an inclined plate,including the Landau-Levich-Derjaguin film,dimple and capillary shock.Dependence of these structures on the inclination angle and relative speed with respect to the plate is discussed in detail.Numerical solutions of the lubrication equation agree well with available asymptotic theory.展开更多
基金supported by Guangdong Provincial Zhujiang Scholar Award Project,National Science Foundation of China(10671163,10871031)the National Basic Research Program under the Grant 2005CB321703Scientific Research Fund of Hunan Provincial Education Department(06A069,06C824)
文摘In this paper,we present a smoothing Newton-like method for solving nonlinear systems of equalities and inequalities.By using the so-called max function,we transfer the inequalities into a system of semismooth equalities.Then a smoothing Newton-like method is proposed for solving the reformulated system,which only needs to solve one system of linear equations and to perform one line search at each iteration. The global and local quadratic convergence are studied under appropriate assumptions. Numerical examples show that the new approach is effective.
文摘In the present paper, we investigate the well-posedness of the global solutionfor the Cauchy problem of generalized long-short wave equations. Applying Kato＇s methodfor abstract quasi-linear evolution equations and a priori estimates of solution,we get theexistence of globally smooth solution.
基金Supported by Natural Science Foundation of China(1077107410771139)+1 种基金Supported by the NSF of Wenzhou University(2007L024)Supported by the NSF of Zhejiang Province(Y6080077)
文摘This paper studies the long time behavior of solutions to the Navier-Stokes equations with linear damping on R^2. The authors prove the existence of L^2-global attractor and Hi-global attractor by showing that the corresponding semigroup is asymptotically compact. Thereafter, they establish that the two attractors are the same and thus reveal the asymptotic smoothing effect of the solutions.
文摘0102258基于卷积的快速分形图像编码[刊]/王冬梅//仪器仪表学报.—2000,21(5).—446～448(E)Y2000-62443-4106 0102259泊松观察的通用平滑方程=A general smoothing equa-tion for poisson observations[会,英]/Malcolm,w.P.＆ Elliott,R.J.//1999 IEEE Decision and Control,Vol.4.～4106-4110(HC)
基金supported by National Natural Science Foundation of China (Grant No.11071029)the Fundamental Research Funds for the Central Universities
文摘We consider a class of mathematical programs governed by parameterized quasi-variational inequalities(QVI).The necessary optimality conditions for the optimization problem with QVI constraints are reformulated as a system of nonsmooth equations under the linear independence constraint qualification and the strict slackness condition.A set of second order sufficient conditions for the mathematical program with parameterized QVI constraints are proposed,which are demonstrated to be sufficient for the second order growth condition.The strongly BD-regularity for the nonsmooth system of equations at a solution point is demonstrated under the second order sufficient conditions.The smoothing Newton method in Qi-Sun-Zhou [2000] is employed to solve this nonsmooth system and the quadratic convergence is guaranteed by the strongly BD-regularity.Numerical experiments are reported to show that the smoothing Newton method is very effective for solving this class of optimization problems.
基金supported by Hong Kong Research Grant Council(Grant No.Poly U5001/12p)National Natural Science Foundation of China(Grant No.11101231)
文摘We propose a smoothing trust region filter algorithm for nonsmooth nonconvex least squares problems. We present convergence theorems of the proposed algorithm to a Clarke stationary point or a global minimizer of the objective function under certain conditions. Preliminary numerical experiments show the efficiency of the proposed algorithm for finding zeros of a system of polynomial equations with high degrees on the sphere and solving differential variational inequalities.
基金supported by National Natural Science Foundation of China(Grant Nos.11171026 and 11271175)National Natural Science Foundation of Shandong Province(Grant No.ZR2012AQ026)
文摘This paper is intended as an attempt to set up the global smoothing for the periodic Benjamin equation. It is shown that for Hs（T） initial data with 8 〉 -1/2 and for any s 〈 s1〈 min{s ＋ 1,3s ＋ 1}, the difference of the evolution with the linear evolution is in Hs1 （T） for all times, with at most polynomial growing HS1 norm. Unlike Korteweg-de Vries （KdV） equation, there are less symmetries of the Benjamin system, especially for the resonant function. The new ingredient is that we need to deal with some new difficulties that are caused by the lack of symmetries.
基金supported by National Natural Science Foundation of China (Grant Nos.10831008,11025107)Fundamental Research Funds for Central Universities (Grant No 2010-34000-3162643)High Level Talent Project in High Schools in Gongdong Province (Grant No 34000-5221001)
文摘In this paper,we prove a general existence theorem of Khler-Einstein metrics on complete Khler manifolds.We use the heat equation method smoothing certain positive (1,1) current in the canonical class.
基金Project supported by the National Natural Science Foundation of China(No.11101188)
文摘The smoothness of the solutions to the full Landau equation for Fermi-Dirac particles is investigated.It is shown that the classical solutions near equilibrium to the Landau-Fermi-Dirac equation have a regularizing effects in all variables (time,space and velocity),that is,they become immediately smooth with respect to all variables.
基金supported by National Natural Science Foundation of China (Grant No. 10701064, 10931001)XINXING Project of Zhejiang University
文摘Let T^2 be a flat two-dimensional torus with fundamental cell domain [-1/2,1/2]×[-1/2,1/2],h（x） a positive smooth function satisfying the symmetric property （8） on T^2.In this paper we give some sufficient condition under which the mean field equation △u = 16π - 16πe^u, has a smooth solution.
基金Project supported by the National Natural Science Foundation of China(No.10071067)and the Jiangsu Provincial Natural Science Foundation of China.
文摘Consider the motion of immersed hypersurfaces driven by surface diffusion flow and give anlower bound on the life span of a smooth immersed solution, which depends only on how muchthe curvature of the initial surface is concentrated in space.
基金the National Natural Science Foundation of China(Grant Nos.11972340,11932019,and 11621202).
文摘It is known that free-surface flows with small slopes can be described by classical lubrication theory.By replacing the assumption of quasi-parallel flows with local wedge flows,the classical lubrication theory has been generalized to the situation with finite surface slopes and vanishing fluxes,e.g.,steady capillary flows with moving contact lines.In this work,this theory is further extended by imposing the contribution of finite fluxes,which can be modeled by a source/sink flow in a wedge.The resulting lubrication equation is used to investigate the surface morphologies observed in dip coating of an inclined plate,including the Landau-Levich-Derjaguin film,dimple and capillary shock.Dependence of these structures on the inclination angle and relative speed with respect to the plate is discussed in detail.Numerical solutions of the lubrication equation agree well with available asymptotic theory.
