Time global structure of solutions of nonlinear conservation law with viscosity and relaxation

成功提出了几种新的加权能量方法来对解进行先验估计。借助这些方法，对非凸通量标量粘性守恒定律解、粘性理想气体方程组、耗散波动方程等大时间行为的分析取得了很大进展。对于半导体模型方程，稳态解的存在性、唯一性和渐近稳定性分析、多个物理参数的层次结构以及数值计算方法也取得了很大进展。

Several new weighted energy methods were successfully proposed to have a priori estimates of solutions. With the aid of these methods, has been much progressed the analysis on the large time behaviors of the solutions of scalar viscous conservation law with non-convex flux, system of equations of viscous ideal gas, dissipative wave equations, etc. Also for model equations of semiconductor, the analysis on existence, uniqueness and asymptotic stability of stationary solutions, hierarchy structures with respect to several physical parameters, and methods of numerical computation has been much progressed.