On the Convergence of Broyden-Like Methods

The author provides a finer local as well as semilocM convergence analysis of a certain class of Broyden-like methods for solving equations containing a nondifferentiable term on the m-dimensional Euclidean space （m ≥ 1 a natural number）.     

Global Attractors and Determining Modes for the 3D Navier-Stokes-Voight Equations

The authors investigate the long-term dynamics of the three-dimensional Navier- Stokes-Voight model of viscoelastic incompressible fluid. Specifically, upper bounds for the number of determining modes are derived for the 3D Navier-Stokes-Voight equations and for the dimension of a global attractor of a semigroup generated by these equations. Viewed from the numerical analysis point of view the authors consider the Navier-Stokes-Voight model as a non-viscous （inviscid） regularization of the three-dimensional Navier-Stokes equations. Furthermore, it is also shown that the weak solutions of the Navier-Stokes- Voight equations converge, in the appropriate norm, to the weak solutions of the inviscid simplified Bardina model, as the viscosity coefficient v →0.     

NONEXISTENCE OF PSEUDO-SELF-SIMILAR SOLUTIONS TO INCOMPRESSIBLE EULER EQUATIONS

In this paper we study a generalization of self-similar solutions. We show that just as for the solutions to the Navier-Stokes equations these supposedly singular solution reduce to the zero solution.In this paper we study a generalization of self-similar solutions. We show that just as for the solutions to the Navier-Stokes equations these supposedly singular solution reduce to the zero solution.     

Stability for the Timoshenko Beam System with Local Kelvin-Voigt Damping

In this paper, we consider a vibrating beam with one segment made of viscoelastic material of a Kelvin-Voigt （shorted as K-V） type and other parts made of elastic material by means of the Timoshenko model. We have deduced mathematical equations modelling its vibration and studied the stability of the semigroup associated with the equation system. We obtain the exponential stability under certain hypotheses of the smoothness and structural condition of the coefficients of the system, and obtain the strong asymptotic stability under weaker hypotheses of the coefficients.     

Stability of viscous contact wave for compressible navier-stokes system of general gas with free boundary

In this paper, we study the large time behavior of solutions to the nonisentropic Navier-Stokes equations of general gas, where polytropic gas is included as a special case, with a free boundary. First we construct a viscous contact wave which approximates to the contact discontinuity, which is a basic wave pattern of compressible Euler equation, in finite time as the heat conductivity tends to zero. Then we prove the viscous contact wave is asymptotic stable if the initial perturbations and the strength of the contact wave are small. This generalizes our previous result [6] which is only for polytropic gas.     

Remark on Exponential Decay of Ground States for N-Laplacian Equations

We study exponential decay property of radial ground states to a class of N-Laplacian elliptic equations in the whole space R^N. Their decay rates as /x/→∞ are obtained explicitly.     

Nonlinearly Coupled KdV Equations Describing the Interaction of Equatorial and Midlatitude Rossby Waves

Amplitude equations governing the nonlinear resonant interaction of equatorial baroclinic and barotropic Rossby waves were derived by Majda and Biello and used as a model for long range interactions （teleconnections） between the tropical and midlatitude troposphere. An overview of that derivation is nonlinear wave theory, but not in atmospheric presented and geared to readers versed in sciences. In the course of the derivation, two other sets of asymptotic equations are presented： the long equatorial wave equations and the weakly nonlinear, long equatorial wave equations. A linear transformation recasts the amplitude equations as nonlinear and linearly coupled KdV equations governing the amplitude of two types of modes, each of which consists of a coupled tropical/midlatitude flow. In the limit of Rossby waves with equal dispersion, the transformed amplitude equations become two KdV equations coupled only through nonlinear fluxes. Four numerical integrations are presented which show （i） the interaction of two solitons, one from either mode, （ii） and （iii） the interaction of a soliton in the presence of different mean wind shears, and （iv） the interaction of two solitons mediated by the presence of a mean wind shear.     

ON A CONSTRUCTION OF INERTIAL MANIFOLDS FOR A CLASS OF SECOND ORDER IN TIME EVOLUTION EQUATIONS

Inertial manifolds for a class of second order in time dlssipative equations are constructed.The author also proves an asymptotic completeness property for the inertlal manifolds andcharcterizes the inertlal manifolds as the set of trajectories whose growth is at most of orderO(e-ut) for some u＞O. As applications, a nonllnear wave equation and a problem of nonlinearoscillations of a shallow shell are considered.     

A GENERALIZED QUASI-NEWTON EQUATION AND COMPUTATIONAL EXPERIENCE

The quasi-Newton equation has played a central role in the quasi-Newton methods forsolving systems of nonlinear equations and/or unconstrained optimization problems.In-stead,Pan suggested a new equation,and showed that it is of the second order while thetraditional of the first order,in certain approximation sense[12].In this paper,we makea generalization of the two equations to include them as special cases.The generalizedequation is analyzed,and new updates are derived from it.A DFP-like new update out-performed the traditional DFP update in computational experiments on a set of standardtest problems.     

DIRECT CONSTRUCT OF PERIODIC SOLUTIONS TO PERTURBED KLEIN-GORDON EQUATIONS BY NEWTON ITERATION

61. IntroductionNear an equilibrium state to a system of nonlinear ODEs, one can regard the nonlinearsystem as a perturbation of its linearization. It is well known that if none of the characteristicexponents of the linearized system has zero real part, then the phase portrait near theequilibrium of the nonlinear system is topologically equivalent to that of its linearization(cL [181). However, if characteristic exponents with zero real part appearl then the linearizedsystem alone does not c…     

具偏差变元的广义平均曲率方程同宿解的存在性

In this paper, by using Mawhin＇s continuation theorem and some analysis methods,the existence of a set with 2kT-periodic solutions for a kind of prescribed mean curvature equation with a deviating argument is studied, and then a homoclinic solution is obtained as a limit of a certain subsequence of the above set.     

一类非线性演化方程族的可积耦合

Starting from a Tu Guizhang‘s isospectral‘problem, a Lax pair is obtained by means of Tu scheme ( we call it Tu Lax pair ). By applying a gauge transformation between matrices, the Tu Lax pair is changed to its equivalent Lax pair with the traces of spectral matrices being zero, whose compatibility gives rise to a type of Tu hierarchy of equations. By making use of a high order loop algebra constructed by us, an integrable coupling system of the Tu hierarchy of equations are presented. Especially, as reduction cases, the integrable couplings of the celebrated AKNS hierarchy, TD hierarchy and Levi hierarchy are given at the same time.     

Manakov方程和导数Manakov方程的有限参数解

Finite-dimensional integrable Hamiltonian systems, obtained through the non- linearization of the 3×3 spectral problems associated with the Manakov and the derivative Manakov equations, are investigated. A generating function method is used to give a simple and effective way to prove the involutivity of integrals. Finite-parameter solutions of the Manakov and the derivative Manakov equations are calculated based on the commutative systems of ordinary differential equations with these integrals as Hamiltonians.     

DECAY RATES AND CONVERGENCE OFSOLUTIONS TO SYSTEM OF ONE-DIMENSIONAL VISCOELASTIC MODEL WITH DAMPING

This paper considers the asymptotic behavior of solutions to the system of one-dimensional viscoelastic model with damping and prove that the corresponding solutions time-asymptotically behave like nonlinear diffusion wave as in [4,11]. In addition, It is also shown that the system of one-dimensional viscoelastic model with damping is a viscosity approximation of a hyperbolic conservation laws with damping.     

有关M.S.Berger问题的注记

In this paper, we discuss the problem concerning global and local structure of solutions of an operator equation posed by M. S. Berger. Let f : U 真包含 E → F be a C1 map, where E and F are Banach spaces and U is open in E. We show that the solution set of the equation f(x) = y for a fixed generalized regular value y of f is represented as a union of disjoint connected C1 Banach submanifolds of U, each of which has a dimension and its tangent space is given. In particular, a characterization of the isolated solutions of the equation f(x) = y is obtained.     

MAURER-CARTAN EQUATION OF A∞-ALGEBRAS

The axioms of A∞-algebras can be written as Maurer-Cartan equation. Infinitesimal multiplication of a graded associative algebra is defined and the integrability of infinitesimal multiplication is discussed through the Massey F-product.     

Existence and Asymptotic Behavior of Radially Symmetric Solutions to a Semilinear Hyperbolic System in Odd Space Dimensions

This paper is concerned with a class of semilinear hyperbolic systems in odd space dimensions. Our main aim is to prove the existence of a small amplitude solution which is asymptotic to the free solution as t→-∞in the energy norm, and to show it has a free profile as t→ ∞. Our approach is based on the work of [11]. Namely we use a weighted L∞norm to get suitable a priori estimates. This can be done by restricting our attention to radially symmetric solutions. Corresponding initial value problem is also considered in an analogous framework. Besides, we give an extended result of [14] for three space dimensional case in Section 5, which is prepared independently of the other parts of the paper.     

A Class of Nonlinear Degenerate Parabolic Equations Not in Divergence Form

This paper is devoted to the study of a class of singular nonlinear diffusion problem. The existence and uniqueness of solutions are obtained. Moreover, some properties of solutions such as blow-up property etc. are also discussed.     

A NEW SMOOTHING EQUATIONS APPROACH TO THE NONLINEAR COMPLEMENTARITY PROBLEMS

The nonlinear complementarity problem can be reformulated as a nonsmooth equation. In this paper we propose a new smoothing Newton algorithm for the solution of the nonlinear complementarity problem by constructing a new smoothing approximation function. Global and local superlinear convergence results of the algorithm are obtained under suitable conditions. Numerical experiments confirm the good theoretical properties of the algorithm.     

Dynamical Behaviors in a Two-dimensional Map

We consider the dynamics of a two-dimensional map proposed by Maynard Smith as a population model. The existence of chaos in the sense of Marotto‘s theorem is first proved, and the bifurcations of periodic points are studied by analytic methods. The numerical simulations not only show the consistence with the theoretical analysis but also exhibi the complex dynamical behaviors.