Exact Null Controllability of a Nonlinear Thermoelastic Contact Problem

We study the controllability properties of a nonlinear parabolic system that models the temperature evolution of a one-dimensional thermoelastic rod that may come into contact with a rigid obstacle. Basically the system dynamics is described by a one-dimensional nonlocal heat equation with a nonlinear and nonlocal boundary condition of Newmann type. We focus on the control problem and treat the case when the control is distributed over the whole space domain. In this case the system is proved to be exactly null controllable provided the parameters of the system are smooth. The proof is based on changing the control variable and using Aubins Compactness Lemma to obtain an invariant set for the linearized controllability map. Then, by proving that the found solution is sufficiently smooth, we get the null controllability for the original system.     

耦合热弹性问题的一般解

从线性化后的耦合热弹性基本方程出发,导出了一种新型式的一般解.在拟静态问题时,比Biot的解更简单,少一个势函数.     

Existence of Periodic Solutions for the Quasi-Static Thermoelastic Thermistor Problem

We deal with a new model for the thermistor problem formulated as a coupled system of PDE’s involving nonlinear energy heat equation, stationary charge conservation equation of electrical current and thermoelastic equations of displacement. We establish the existence of weak periodic solutions rewriting our system as an abstract problem in order to utilize the maximal monotone mappings theory and a fixed point argument for a suitable operator equation.      

非自治半线性热黏弹性问题的一致吸引子的维数(英文)

In this paper, we prove the existence of a uniform attractor for the process associated with a non-antonomous semilinear thermoelastic problem. And under the certain parameter, we obtain an upper bound for the Hausdorff dimension of the uniform attractor.     

Homogenization of a Model Problem on Contact Angle Dynamics

In this paper we consider homogenization of oscillating free boundary velocities in periodic media, with general initial data. We prove that there is a unique and stable effective free boundary velocity in the homogenization limit.     

Spatial Stability for the Quasi-Static Problem in Thermoelastic Diffusion Theory

In this paper we derive some spatial stability results for the quasi-static problem in thermoelastic diffusion theory for anisotropic media. The coupled system of equations of thermoelasticity with diffusion is a coupling of an elliptic equation with two parabolic equations. It poses some new mathematical difficulties. Here we study the exponential spatial decay of solutions. An upper bound for the amplitude in terms of the boundary and initial conditions is obtained. The extension of the spatial stability results is also treated.     

Signorini接触问题的边界变分不等式

本以Signorini接触问题为背景，讨论了变分不等式与边值问题的等价性，利用Green公式，基本解和基本解法向导数的性质，将区域型变分不等式化成等价的边界型变分不等式，并证明了边界变分不等式解的存在唯一性，为使用边界元方法数值求解提供理论依据。     

具有局部阻尼的热弹性问题的渐近行为和指数稳定性

一个关于具有局部阻尼的半线性热弹性问题,是材料科学中最重要的数学模型之一．这个问题的解的存在性和齐次问题解的指数衰竭于零的性质被得到了．进而,也得到了对非齐次问题吸收集的存在性．结果显示了所研究的系统是渐近稳定的．     

General Decay for a Thermoelastic Problem of a Microbeam with Gurtin-Pipkin Thermal Law

In this paper, we study the well-posedness and the asymptotic stability of a one-dimensional thermoelastic microbeam system, where the heat conduction is given by Gurtin-Pipkin thermal law. We first establish the well-posedness of the system by using the semigroup arguments and Lumer-Phillips theorem. We then obtain an explicit and general formula for the energy decay rates through perturbed energy method and some properties of the convex functions.