Mathematical Sciences: Penalization Techniques for the Studyof Free and Moving Boundaries

该奖项将为Juan Redondo提供支持，他是一名 密歇根大学的博士后， 劳赫 雷东多博士计划继续研究 抛物型变分方程解中的自由边界 与经典Stefan不等式类似的不等式 问题. 他还将研究休克的规律性 双曲型守恒律的波动解 变分技术的抛物系统，来自 在原双曲方程组中加入粘性项。 非线性偏微分方程描述了许多 热流动等耗散现象。 的量是否 耗散很小，这类方程的解通常表现为 仿佛根本没有消散。在这个授予博士后， Juan Redondo将使用变分理论中的技术， 利用耗散和非耗散之间的关系 为了研究边界的形状 不同材料之间的差异， 不同密度的气体。

This award will provide support for Juan Redondo, who is a postdoc at the University of Michigan working with Professor Jeff Rauch. Dr. Redondo plans to continue his study of the regularity of free boundaries in the solutions of parabolic variational inequalities like the ones associated with the classical Stefan problem. He is also going to investigate the regularity of shock wave solutions of hyperbolic conservation laws by applying his variational techniques to the parabolic systems that come from adding viscous terms to the original hyperbolic systems. Nonlinear partial differential equations describe many dissipative phenomena like the flow of heat. If the amount of dissipation is small the solutions of such equations often behave as if there is no dissipation at all. In this grant the postdoc, Juan Redondo, will use techniques from variational theory that exploit this relationship between dissipative and non-dissipative systems in order to study things like the shape of a boundary between different materials and the sharpness of a front between gases of different densities.