Mathematical Sciences: Analysis of Cavitation

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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.