Hele-Shaw type problems with dynamical boundary conditions

In this paper, we study the nonlinear evolution equation of Hele-Shaw type with dynamical boundary conditions. That is, the equation ut=Δw+f where u∈H(w) and H is the Heaviside function, with boundary condition μ(x,w)t_∂w+k∇w⋅ν=g, where ν denotes the outward normal vector of the fixed boundary of the domain. We prove existence, uniqueness and some qualitative properties of the solution.     

Oscillation of certain partial difference equations

In this paper we consider a class of nonlinear delay partial difference equations and a class of linear delay partial difference equations with variable coefficients, which may change sign. We obtain oscillation criteria for these equations. There are no results for the oscillation of these equations up to now.     

Proximality and Chebyshev sets

This paper is a companion to a lecture given at the Prague Spring School in Analysis in April 2006. It highlights four distinct variational methods of proving that a finite dimensional Chebyshev set is convex and hopes to inspire renewed work on the open question of whether every Chebyshev set in Hilbert space is convex.     

深能级杂质对光导半导体开关非线性特性的影响

建立了非线性GaAs光导开关深能级杂质瞬态模型的基本方程,获得了与实验现象定性吻合的电流输出,给出了平均载流子随时间演化的情况.分析结果表明,在考虑了深能级杂质的俘获、发射和碰撞电离后,有可能对非线性光导开关中发生的一系列现象做出解释,进一步的仔细分析将对非线性光导开关的设计和制作提供理论指导.     

Discrete global descent method for discrete global optimization and nonlinear integer programming

A novel method, entitled the discrete global descent method, is developed in this paper to solve discrete global optimization problems and nonlinear integer programming problems. This method moves from one discrete minimizer of the objective function f to another better one at each iteration with the help of an auxiliary function, entitled the discrete global descent function. The discrete global descent function guarantees that its discrete minimizers coincide with the better discrete minimizers of f under some standard assumptions. This property also ensures that a better discrete minimizer of f can be found by some classical local search methods. Numerical experiments on several test problems with up to 100 integer variables and up to 1.38 × 10¹⁰⁴ feasible points have demonstrated the applicability and efficiency of the proposed method.     

Sharp condition of global existence for second-order derivative nonlinear Schrödinger equations in two space dimensions

This paper discusses a class of second-order derivative nonlinear Schrödinger equations which are used to describe the upper-hybrid oscillation propagation. By establishing a variational problem, applying the potential well argument and the concavity method, we prove that there exists a sharp condition for global existence and blow-up of the solutions to the nonlinear Schrödinger equation. In addition, we also answer the question: how small are the initial data, the global solutions exist?     

Oscillation of solutions of second-order nonlinear differential equations of Euler type

We consider the nonlinear Euler differential equation t²x^″+g(x)=0. Here g(x) satisfies xg(x)>0 for x≠0, but is not assumed to be sublinear or superlinear. We present implicit necessary and sufficient condition for all nontrivial solutions of this system to be oscillatory or nonoscillatory. Also we prove that solutions of this system are all oscillatory or all nonoscillatory and cannot be both. We derive explicit conditions and improve the results presented in the previous literature. We extend our results to the extended equation t²x^″+a(t)g(x)=0.     

A geometric theory forL 2-stability of the inverse problem in a one-dimensional elliptic equation from anH 1-observation

This study provides a stability theory for the nonlinear least-squares formulation of estimating the diffusion coefficient in a two-point boundary-value problem from an error-corrupted observation of the state variable. It is based on analysing the projection of the observation on the nonconvex attainable set.This research was started while G. Chavent visited the Technical University of Graz. Support through the Steiermaerkische Landesregierung is gratefully acknowledged.     

A molecular network model to describe the nonlinear viscoelastic behavior of polymers

A transient molecular network model is built to describe the nonlinear viscoelasticity of polymers by considering the effect of entanglement loss and regeneration on the relaxation of molecular strands. It is an extension of previous network theories. The experimental data on three thermoplastic polymers (ABS, PVC and PA6) obtained under various loading conditions are used to test the model. Agreement between the theoretical and experimental curves shows that the suggested model can describe successfully the relaxation behavior of the thermoplastic polymers under different loading rates by using relatively few relaxation modes. Thus the micromechanism responsible for strain-rate dependence of relaxation process and the origin of nonlinear viscoelasticity may be disclosed. The project supported by the National Natural Science Foundation of China and Doctorial Fund