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

包含大波浪的解附近守恒定律系统的适定性

• 批准号: 0600371
• 负责人: Marta Lewicka
• 金额: $ 1.91万
• 依托单位: University of Minnesota-Twin Cities
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-09-01 至 2007-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0600371&HistoricalAwards=false
• 关键词: Well; Posedness; Systems; Conservation; Laws

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.

该提案将为严格双曲守恒定律系统产生的波动模式建立有界性和可积性结果。这些方法适用于作为一维黎曼和柯西问题的解而生成的非相互作用冲击波和稀疏波模式，对其振幅没有任何限制。至于该项目更广泛的影响，项目负责人希望将获得的分析结果与最近发现某些重气体的有限变化不稳定性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。