Advances in Modern Free Boundary Problems

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Advances in Modern Free Boundary ProblemsAbstract of Proposed ResearchEduardo V Teixeira This project is to study free boundary problems that arise in science. One problem is to study mathematical models of the optimal shape of an heterogeneous body with respect insulation. That is one wishes to minimize the heat flux as a function of shape for the same exterior conditions. This model also corresponds to a number of other physical optimization problems. Another project is to study certain free boundary problems that arise in combustion theory and the propagation of flame fronts. Mathematically these problems involve the existence, regularity and stability of free boundaries and of the solutions of the systems of equations that model these phenomena. The PI proposes to develop new analytical and geometrical methods for analyzing these problems.