Well Posedness of Systems of Conservation Laws Near Solutions Containing Large Waves

该建议将建立有界性和可积性的结果所产生的严格双曲系统的守恒律的波图案。该方法适用于图案的非相互作用的冲击和稀疏波产生的一维黎曼和柯西问题的解决方案，没有任何限制，其振幅。至于该项目的更广泛的影响，PI希望将获得的分析结果与最近的实验数据联系起来，在这些数据中发现了某些重气体的有限变化不稳定性。这些发现将在天文学和天体物理学领域产生影响。

The proposal will establish boundedness and integrability results for wave patterns arising from strictly hyperbolic systems of conservation laws. The methods apply to patterns of non-interacting shock and rarefaction waves generated as solutions of the one-dimensional Riemann and Cauchy problems without any restrictions on their amplitude. As to the project's broader impacts, the PI is hoping to link the analytical results obtained to recent experimental data where the bounded variation instabilities of certain heavy gases have been discovered. These findings will have impact in the fields of astronomy and astrophysics.