Abstract:

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. 

Key words: piston problem; pressure gradient equations; shock wave solution; Glimm scheme