Mixed variational formulations in locally convex spaces

The main purpose of this paper is to extend to the setting of locally convex spaces the study of the mixed variational formulation of some elliptic boundary value problems, the so-called Babuška–Brezzi theory. This study consists of characterizing the existence of a solution and giving conditions that guarantee the stability of the corresponding Galerkin method.     

Cn中多圆柱体的Riemann-Hilbert边值问题

本文研究了利用Poission核求解C^N（1≤n≤2）中单位多圆柱体上Riemann-Hilbert边值问题．同时，给出了其解的表达式和可解条件，并将原来求解空间从解析函数空间推广到亚纯函数空间．     

On the regularity of American options with regime-switching uncertainty

We study the regularity of the stochastic representation of the solution of a class of initial–boundary value problems related to a regime-switching diffusion. This representation is related to the value function of a finite-horizon optimal stopping problem such as the price of an American-style option in finance. We show continuity and smoothness of the value function using coupling and time-change techniques. As an application, we find the minimal payoff scenario for the holder of an American-style option in the presence of regime-switching uncertainty under the assumption that the transition rates are known to lie within level-dependent compact sets.     

一类差分系统边值问题在渐近线性下的多解存在性

应用临界点理论,获得了一类差分系统边值问题在渐近线性下存在多个非平凡解的条件.     

Lyapunov inequalities for partial differential equations

This paper is devoted to the study of Lp Lyapunov-type inequalities (1?p?+∞) for linear partial differential equations. More precisely, we treat the case of Neumann boundary conditions on bounded and regular domains in RN. It is proved that the relation between the quantities p and N/2 plays a crucial role. This fact shows a deep difference with respect to the ordinary case. The linear study is combined with Schauder fixed point theorem to provide new conditions about the existence and uniqueness of solutions for resonant nonlinear problems.     

Boundary feedback stabilization of coupled sine-Gordon equations

^** Email: koba{at}cntl.kyutech.ac.jp^*** Email: sakamoto{at}cntl.kyutech.ac.jp This paper is concerned with global stabilization of the systemgoverned by coupled sine-Gordon equations without damping. Astabilizer is constructed by boundary velocity feedback. Theclosed-loop system is shown to be well posed by the non-linearsemigroup approach. Moreover, using a multiplier method, globalexponential stabilization of the closed-loop system is proved.     

Time-dependent coating flows in a strip, Part I: The linearized problem

This work is concerned with time-dependent coating flow in a strip . The Navier-Stokes equations are satisfied in the fluid region, the bottom substrate is moving with fixed velocity , and fluid is entering the strip through the upper boundary . The free boundary has the form for , where is the moving contact point. Our objective is to prove that if the initial data are close to those of a stationary solution (the existence of such a solution was established by the authors in an earlier paper) then the time-dependent problem has a unique solution with smooth free boundary, at least for a small time interval. In this Part I we study the linearized problem, about the stationary solution, and obtain sharp estimates for the solution and its derivatives. These estimates will be used in Part II to establish existence and uniqueness for the full nonlinear problem.

     

应变对纳米铜晶界迁移的影响

用分子动力学方法模拟了金属铜纳米双晶中晶界在应变作用下的迁移过程,晶界类型为〈11l〉倾侧∑19晶界。原子问相互作用力采用Finnis-Sinclair型EAM势计算。结果表明：平行于晶界方向的压应变可以促进晶界在相邻品界交互作用下发生迁移;垂直于晶界方向的压应变则不能对晶界迁移产生明显的效果。晶界迁移大致可分为两个阶段,前阶段晶界迁移缓慢,随晶界间距减小,晶界间交互作用加强,使晶界迁移显著加速。