Multidimensional Conservation Laws and Low Regularity Solutions

多维守恒定律和低正则解

• 批准号: 0306307
• 负责人: Barbara Keyfitz
• 金额: $ 17.9万
• 依托单位: University of Houston
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-08-01 至 2006-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0306307&HistoricalAwards=false
• 关键词: Multidimensional; Conservation; Laws; Low; Regularity

Free boundary problems arising in shock reflection have been solved for regular shockreflection in a model equation; the method will be extended to a larger set of equations andother types of shock reflection. Solving a prototype problem for the gas dynamics equationsis in sight. Other two-dimensional Riemann problems, such as reflection of rarefaction wavesat the sonic line, will be considered. A different free boundary problem, with connections tonew kinds of singularities, occurs in this case. By constrast with shock reflection problems,in which the complicated behavior occurred in the subsonic region and was analysed usingHolder estimates for degenerate elliptic equations, the interaction of rarefaction waves withthe sonic boundary involves study of degenerate hyperbolic eigenvalue problems.The PI has had success, particularly with women graduate students and postdoctoralvisitors, in introducing beginning researchers to her areas in conservation laws, and in helpingto expand their career horizons. It is planned to mentor two postdocs (at least one, alreadyselected, is a woman), including encouraging their teaching and professional development inways such as writing proposals, refereeing papers, and participating in conferences.In addition, the second research topic is strongly interdisciplinary, and the PI's work hasaroused some positive interest in the multifluid science community. The PI and co-workerswill attend and make presentations at engineering conferences, write articles for journals onmultiphase flow to explain the results, and organize sessions at conferences to bring togethermathematical, computational and experimental researchers in multifluid science.

在冲击反射中引起的自由边界问题已解决，以在模型方程式中进行常规的冲击反射。该方法将扩展到较大的方程和其他类型的冲击反射。在视线中解决气体动力学方程的原型问题。将考虑其他二维Riemann问题，例如Sonic线的反射。在这种情况下，发生了不同的自由边界问题，并带有连接音调的奇异性。通过与冲击反射问题的约束，在亚音速区域中发生了复杂行为，并使用持有人的估算值对退化的椭圆方程式进行了估算，稀疏浪潮与声音边界的相互作用涉及对脱发双重征收特征性问题的研究。扩大他们的职业视野。计划指导两个博士后（至少一个是Alreadyseyseleds，是一个女性），包括鼓励他们的教学和专业发展，例如撰写建议，裁判论文和参与会议。此外，第二个研究主题是强烈的跨学科，以及PI的工作对多方面的综合科学群体的积极兴趣。 PI和同事将在工程会议上参加并进行演讲，为期刊上写文章，以解释结果，并在会议上组织会议，以带来多流体科学中的togethermathemathemathemathemathemathemathemathemathemathemathemathemathemathemathemathemathemathemathemathemathemathemathemathemathemathemathemathemathemathemathemathemathemathemathemathemathemathemathemathemathemathemathemathemathemathemathiphase。