可压缩Euler-Maxwell方程解的性态研究

等离子体是宇宙中物质存在的主要形式，可压缩Euler-Maxwell方程把等离子体看成导电流体，用经典流体力学和电动力学相结合的方法来描述等离子体的运动，是等离子体的宏观理论。其数学理论的研究逐步引起了数学界的关注。对这类方程的研究，不仅有重大的理论意义，而且随着问题的解决也必将会对解释某些物理现象提供重要的参考。本项目拟围绕一维可压缩Euler-Maxwell方程非线性扩散波的稳定性以及三维可压缩Euler-Maxwell方程带有物理边界条件有界域内解的存在性和大时间行为等方面展开系统深入的研究，期望在这些方面取得突破性的进展。

It is believed that most of the matters in the universe are in the form of plasma.Taking plasma as conductive fulid and combining classical hydrodynamics with electrodynamics, Euler-Maxwell equations describe the dynamical evolution of plasma, which can be viewed as macro theory of plasma. Theoretical study of mathematics on compressible Euler-Maxwell equations gradually attracted the attention of many mathematicians. The study of this kind of equation, not only is theoretically significant, but also will provide important reference to explain some physical phenomena. This project is concerned with the stability of nonlinear diffusion wave on one-dimensional compressible Euler-Maxwell equations, as well as the existence and large-time behavior of solution to initial-boudary value problem with physical boundary conditions on three-dimensional compressible Euler-Maxwell equations. We expect a breakthrough in these aspects.