一类一维的辐射流体力学方程组激波的存在性

Existence of a Shock Wave in a One-dimensional Radiation Hydrodynamic System

该文主要讨论一维空间中一类辐射流体力学方程组的激波.由Rankine-Hugoniot条件及熵条件得此问题可表述为关于辐射流体力学方程组带自由边界的初边值问题.首先通过变量代换,将其自由边界转换为固定边界,然后研究关于此非线性方程组的一个初边值问题解的存在唯一性.为此先构造了此问题的一个近似解,然后分别通过Picard迭代与Newton迭代对此非线性问题构造近似解序列.通过一系列估计与紧性理论得到此近似解序列的收敛性,其极限即为原辐射热力学方程组的一个激波.

In this paper,the authors mainly study shock waves in a one-dimensional radiation hydrodynamic system.By using the Rankine-Hugoniot condition and entropy condition,this problem can be formulated as an initial boundary value problem with a free boundary for radiation hydrodynamic system.First,the authors transform this free boundary to the fixed one by using change of variables involving unknowns.Then they investigate the existence and uniqueness of the solution to the initial boundary value problem for this nonlinear system.For this problem,the authors first construct an approximate solution by using the compatibility conditions of the data.Then they use the Picard iteration and the Newton iteration for this nonlinear system respectively to construct a sequence of approximate solutions.By using a series of estimates and a compactness argument,the convergence of the sequence of approximate solutions is obtained.The limit of this sequence gives a shock wave of the original radiation hydrodynamic system.