Abstract: In this paper, we consider the existence of local solutions to a 2-dimensional axially-symmetrical piston problem of pressure-gradient equations. As the problem is axially-symmetric, proper variables first are selected to transform the original problem into a 1-dimensional problem. By Taylor expansion, we construct an N-ordered approximate solution used as the first term in the Newton iterative method. With the Newton iteration and the energy estimation, we show the local existence of the shock front solution to the problem.

Key words: energy estimation, Newton iteration, piston problem, pressure-gradient equations, shock front solution