Abstract
In this paper, we are concerned with the global existence and stability of strong shock front for one-dimensional piston problem. We use the exothermically reacting Euler equations as a mathematical model to describe the gas motion. Under the assumptions that the total variations of initial data and the perturbation of piston velocity are sufficiently small, we establish the global existence and asymptotic behavior of entropy solutions including a strong shock front without restriction on the strength. A modified fractional wave front tracking scheme is developed and a modified Glimm-type functional is carefully designed.
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