一类守恒律方程组周期解的存在性

The Existence of Periodic Solutions to a Class of Conservation Laws

利用改进版本的Glimm格式得到一类源自于等熵多方气体动力学方程组的守恒律方程组周期解的存在性.这类方程组的周期解最早被Frid研究.文中通过对近似解更精细的估计,改进了Frid的结论,得到当周期初值U_0∈L∞∩BV_(loc)(R),方程组存在属于L∞∩BV_(loc)(R×R_+)的周期解U(x,t).首先构造近似解,并得到近似解的有界性和全变差的有界性,然后根据Glimm格式的框架得到周期解的存在性.

In this paper,the existence of periodic solutions to a class of conservation laws via a modified Glimm scheme is obtained. The periodic solutions of such systems are first studied by Frid. The conclusion of Frid is improved by finer estimation of the approximate solution. If the periodic initial data U0∈L∞∩BVloc（R）,there exists a periodic solution U（x,t）,which belongs to L∞∩BVloc（R × R+）. In this paper,Firstly,the approximate solution is constructed,and the boundedness of the approximate solution and the boundedness of the total variation are obtained. Then,the existence of periodic solutions is obtained according to the frame of the Glimm scheme.