压差方程的一维活塞问题

One-Dimensional Piston Problem of Pressure-Gradient Equations

用改进的Glimm格式的方法,研究压差方程的一维活塞问题:当活塞的运动速度是一个常数的扰动时,含有激波的弱解的存在性.对波的相互作用以及扰动波在主激波和活塞上的反射给出了精确的估计,在对主激波的强度不加限制的情况下证明激波解的整体存在性.

This paper uses the improved Glimm scheme to study a one-dimensional problem for the pressure gradient equations when the speed of piston is a constant disturbance. We show existence of the weak solution containing shock waves. Using the modified Glimm scheme, we give global existence of shock front solution to this problem in bounded varition （BV） space.