Existence and uniqueness of global solution to an inverse piston problem

Abstract

In this paper, we consider the generalized Cauchy problem with Cauchy data given on a semi-bounded non-characteristic curve for quasilinear hyperbolic systems. Under suitable assumptions, we obtain the global existence and uniqueness of the C1 solution on the corresponding maximum determinate domain. By means of this result, we globally solve an inverse piston problem for one-dimensional gas dynamics as follows: suppose that the original state of the gas on the right-hand side of the piston and the position of the forward shock are known, then we can globally determine the speed of the piston in a unique manner.