Mathematical Sciences: Analysis of Cavitation

首席研究员将分析数学模型 并将制定标准， 预测这种材料在外力作用下的失效。 的 感兴趣的失败类型是由于形成 尺寸增大并联合收割机形成裂纹的微孔 in the material材料. 将讨论的具体问题包括 孤洞的形成和动态生长， 在一个孤立的表面上形成二次裂纹 洞 从数学上讲，提出的问题涉及分析 一类拟线性椭圆型方程奇异解的存在性 系统，存在，和受理标准， 双曲型方程组的奇异解，以及 微积分中的奇异极小化问题 变化.

The Principal Investigator will analyze mathematical models for certain plastics and metals and will develop criteria to predict the failure of such materials under external forces. The types of failures of interest are those due to the formation of microscopic holes which grow in size and combine to form cracks in the material. Particular problems that will be addressed are the initiation and dynamic growth of a solitary hole, and the formation of secondary cracks upon the surface of a solitary hole. Mathematically, the proposed problems involve the analysis of existence of singular solutions to quasilinear elliptic systems, the existence of, and admissibility criterion for, singular solutions to hyperbolic systems, and the existence of minimizers with singularities for problems in the calculus of variations.