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

该提案将为严格双曲型守恒律系统产生的波型建立有界性和可积性结果。该方法适用于作为一维Riemann和Cauchy问题的解而产生的非相互作用激波和稀疏波的模式，而对其幅度没有任何限制。至于该项目的更广泛影响，PI希望将获得的分析结果与最近发现某些重气体的有界变化不稳定的实验数据联系起来。这些发现将对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.