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.

中文翻译：

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欧拉方程放热反应的一维活塞问题激波前沿解的整体存在性和稳定性

在本文中，我们关注一维活塞问题的强冲击锋的整体存在性和稳定性。我们使用放热反应的欧拉方程作为描述气体运动的数学模型。在初始数据的总变化和活塞速度的摄动足够小的假设下，我们建立了包括强冲击前锋在内的熵解的整体存在性和渐近行为，而对强度没有限制。提出了改进的分数波前跟踪方案，并精心设计了改进的Glimm型函数。