Long time behavior for damped generalized coupled nonlinear wave equations. Ⅱ.Unbounded domain

Introduction In [if, the authors established the unique existence of the smooth solution for the couplednonlinear equations. These were proposed to describe the interaction process of internal longwaves. In [2], Ito proposed a recursion operator by which he inferred that the equations possessinfinitely many symmetries and constants of motion. In [31, He established the existence ofa smooth solution to the system of coupled nonlinear KdV equations[41. We remark that'Schonbeh[sl dealt with a …     

On the global existence of smooth solutions to the multi-dimensional compressible euler equations with time-depending damping in half space

This paper is a continue work of [4, 5]. In the previous two papers, we studied the Cauchy problem of the multi-dimensional compressible Euler equations with time-depending damping term -μ/((1+t)λ)ρu, where λ≥ 0 and μ 0 are constants. We have showed that, for all λ≥ 0 and μ 0, the smooth solution to the Cauchy problem exists globally or blows up in finite time. In the present paper, instead of the Cauchy problem we consider the initialboundary value problem in the half space R_+~d with space dimension d = 2, 3. With the help of the special structure of the equations and the fluid vorticity, we overcome the difficulty arisen from the boundary effect. We prove that there exists a global smooth solution for 0 ≤λ 1when the initial data is close to its equilibrium state. In addition, exponential decay of the fluid vorticity will also be established.     

Smooth Solution to the 1-Dimensional Spin Equations of Antiferromagnets

In this paper, the global existence and uniqueness of a smooth solution to the periodic initial-value problem of the spin equations of antiferromagnets in 1 dimension are proved.     

THE EXISTENCE OF POSITIVE SOLUTIONS TO BOUNDARY VALUE PROBLEM OF SECOND ORDER DIFFERENTIAL EQUATIONS

In this paper, a fixed point theorem in C1[0,1] space is established using the properties of the fixed point index. This theorem is applied to prove the existence of positive solution to the boundary value problems of second order differential equations.     

Partially time-varying coefficient linear rate model for the recurrent event data

In [13], Schaubel et al. proposed a semiparametric partially linear rate model for the statistical analysis of recurrent event data. But they only considered the model with time-independent covariate effects. In this paper, rate function of the recurrent event is modeled by a semipaxametric partially linear function which can include the time-varying effects. We propose the method of generalized estimating equations to make inferences about both the time-varying effects and time-independent effects. The large sample properties are established, while extensive simulation studies are carried out to examine the proposed procedures. At last, we apply the procedures to the well-known bladder cancer study.     

On Compressible Smooth Viscous Fluids in Slowly Expanding Balls

In[17]and[19,20],the global existence and large time behaviors of smooth compressible fluids(including inviscid gases of Euler equations,viscous gases of Navier-Stokes equations,and rarified gases of Boltzmann equation,respectively)have been established in an infinitely expanding ball with a constant expansion speed.This paper concerns with the viscous fluids in a slowly expanding ball.By involved analy-sis on the density function and the weighted energy estimates,we show that the fluid in the slowly expanding ball smoothly tends to a vacuum state and there is no appearance of vacuum in any part of the expansive ball.Our present result is a meaningful supplement to the one in[19].     

Mather theory for piecewise smooth Lagrangian systems

We establish the Mather theory for a type of piecewise smooth and positive definite Lagrangian systems.It models a mechanical system subject to external impulsive forcing.We show the existence of the minimal measure and the Lipschitz property of Aubry set.In addition,the weak KAM solution to this kind of piecewise smooth Lagrangian is also established.     

A QP Free Feasible Method

In [12], a QP free feasible method was proposed for the minimization of a smooth function subject to smooth inequality constraints. This method is based on the solutions of linear systems of equations, the reformulation of the KKT optimality conditions by using the Fischer-Burmeister NCP function. This method ensures the feasibility of all iterations. In this paper, we modify the method in [12] slightly to obtain the local convergence under some weaker conditions. In particular, this method is implementable and globally convergent without assuming the linear independence of the gradients of active constrained functions and the uniformly positive definiteness of the submatrix obtained by the Newton or Quasi Newton methods. We also prove that the method has superlinear convergence rate under some mild conditions. Some preliminary numerical results indicate that this new QP free feasible method is quite promising.     

Global smooth solutions to relativistic Euler-Poisson equations with repulsive force

In this paper, we are concerned with the global existence of smooth solutions for the one dimen- sional relativistic Euler-Poisson equations： Combining certain physical background, the relativistic Euler-Poisson model is derived mathematically. By using an invariant of Lax＇s method, we will give a sufficient condition for the existence of a global smooth solution to the one-dimensional Euler-Poisson equations with repulsive force.     

Zero dissipation limit of the compressible heat-conducting navier-stokes equations in the presence of the shock

The zero dissipation limit of the compressible heat-conducting Navier–Stokes equations in the presence of the shock is investigated. It is shown that when the heat conduction coefficient κ and the viscosity coefficient ε satisfy κ = O（ε）, κ/ε≥ c 〉 0, as ε→ 0 （see （1.3））, if the solution of the corresponding Euler equations is piecewise smooth with shock wave satisfying the Lax entropy condition, then there exists a smooth solution to the Navier–Stokes equations, which converges to the piecewise smooth shock solution of the Euler equations away from the shock discontinuity at a rate of ε. The proof is given by a combination of the energy estimates and the matched asymptotic analysis introduced in [3].     

Random Point Attractors Versus Random Set Attractors

The notion of an attractor for a random dynamical system withrespect to a general collection of deterministic sets is introduced.This comprises, in particular, global point attractors and globalset attractors. After deriving a necessary and sufficient conditionfor existence of the corresponding attractors it is proved thata global set attractor always contains all unstable sets ofall of its subsets. Then it is shown that in general randompoint attractors, in contrast to deterministic point attractors,do not support all invariant measures of the system. However,for white noise systems it holds that the minimal point attractorsupports all invariant Markov measures of the system.     

Uniform attractors for non-autonomous motion equations of viscoelastic medium

Sufficient conditions for existence of minimal uniform trajectory attractors and uniform global attractors of non-autonomous evolution equations in Banach spaces are obtained. It is not assumed that the symbol space of an equation is a compact metric space and that the family of trajectory spaces corresponding to this symbol space is translation-coordinated or closed in any sense. Using these results, existence of minimal uniform trajectory attractors and uniform global attractors for weak solutions of the boundary value problem for motion equations of an incompressible viscoelastic medium with the Jeffreys constitutive law is shown.     

Pullback exponential attractors for the non-autonomous micropolar fluid flows

This paper investigates the pullback asymptotic behaviors for the non-autonomous micropolar fluid flows in 2D bounded domains. We use the energy method, combining with some important properties of the generated processes, to prove the existence of pullback exponential attractors and global pullback attractors and show that they both with finite fractal dimension. Further, we give the relationship between global pullback attractors and pullback exponential attractors.     

Finite Dimensional Behavior for Weakly Damped Generalized KdV-Burgers Equations

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Global attractors for wave equations with nonlinear interior damping and critical exponents

In this paper we study the global attractors for wave equations with nonlinear interior damping. We prove the existence, regularity and finite dimensionality of the global attractors without assuming a large value for the damping parameter, when the growth of the nonlinear terms is critical.     

The Global Attractors for the Periodic Initial Value Problem of Generalized Kuramoto-Sivashinsky Type Equations in Multi-dimensions

The existence of global attractors for the periodic initial value problem of generalized Kuramoto-Sivashinsky type equations in multi-dimensions is proved. We also get the estimates of the upper bounds of Hausdorff and fractal dimensions for the global attractors by means of a uniform priori estimates for time.     

The Global Attractors for Damped Generalized Coupled Nonlinear Wave Equations

The existence of global attractors for the periodic initial value problem of damped generalized coupled nonlinear wave equations is proved. We also get the estimates of the upper bounds of Hausdorff and fractal dimensions for the global attractors by means of a uniformly priori estimates for time.     

The Global Attractors for the Periodic Initial Value Problem For a Coupled Non-linear Wave Equation

The existence of global attractors of the periodic initial value problem for a coupled non-linear wave equation is proved. We also get the estimates of the upper bounds of Hausdorff and fractal dimensions for the global attractors by means of uniform a priori estimates for time.     

Finite dimensionality of the global attractors for von Karman equations with nonlinear interior dissipation

In this paper we study the global attractors for von Karman equations with nonlinear interior dissipation. We prove regularity and then establish finite dimensionality of the global attractors without assuming large values for the damping parameter.     

梁方程时间依赖全局吸引子的存在性

研究了梁方程时间依赖吸引子的存在性,在非线性项f满足临界增长条件时,基于时间依赖全局吸引子的存在性定理,应用先验估计和算子分解方法验证了系数参数与时间t有关时,梁方程对应的过程族{U(t,τ)}的渐近紧性,从而得到梁方程时间依赖全局吸引子的存在性及正则性.