ASYMPTOTIC SOLUTIONS OF THE ELASTIC EQUATION IN THE CASE OF TOTAL REFLECTION

In this paper we construct outgoing asymptotic solutions of the anisotropic elastic wave equation coinciding with given data on the boundary when total reflection happens. In this case the solutions consist of the usual hyperbolic parts and the elliptic parts exponentially decreasing in the normal direction to the boundary. The main assertion is that sum of those parts can cover any boundary data because of the elasticity. The proof is reduced to the complex analysis of the symbol of the elastic operator. By means of the asymptotic solutions we can make parametrices and study propagation of the singularities in the case of total reflection.

     

GLOBAL EXISTENCE OF MILD SOLUTIONS FOR THE ELASTIC SYSTEM WITH STRUCTURAL DAMPING

In this paper, we study the global existence of mild solutions for the semilinear initial-value problems of second order evolution equations, which can model an elastic system with structural damping. This discussion is based on the operator semigroups theory and the Leray-Schauder fixed point theorem.In addition, an example is presented to illustrate our theoretical result.     

具有小周期孔隙复合材料弹性结构的双尺度有限元分析

对于具有小周期孔隙复合材料弹性结构,在双尺度渐近分析理论结果的基础上提出了双尺度有限元计算格式,并给出了严格的误差估计.     

一个超导理论中的反应扩散系统的解析解

A reaction diffusion system arising in the theory of superconductivity is considered and its many kinds of analytic solutions are constructed by the Painlev analysis and similarity reduction methods.     

整周期复合材料弹性结构的双尺度渐近分析

本文讨论了仅包含完整基本构造的小周期弹性结构的双尺度渐近分析方法,并给出了采用有限项表示式的截断误差。