摘要
考虑二维轴对称相对论Euler方程组的活塞问题.利用轴对称的特点,使用适当的变量先将原问题转化为一维问题,然后通过Taylor展开的方法构造原问题的一个N阶近似解,再利用对相应线性问题所作的能量估计,用Newton迭代法,最终证明其活塞问题激波解的局部存在性.
In this paper, we consider a 2-dimensional axially-symmetrical piston problem of relativistic Euler equations. As the problem is axially-symmetric, proper variables are firstly selected to transform the original problem into a 1-dimensional problem. Then, by the Taylor expansion, we construct an N-ordered approximate solution. Using the energy estimate of the solutions to the corresponding linear problem and Newton＇s iteration, we finally obtain the local existence of the shock front solution to the problem.
出处
《应用数学与计算数学学报》
2018年第1期87-105,共19页
Communication on Applied Mathematics and Computation
基金
国家自然科学基金青年科学基金资助项目(11001164
11201289)
