Seminar: Probability and Stochastic Processes Seminar

ECE Women Community

Boundary-free free boundary problems (and particle systems with selection)

Date: May,31,2022 Start Time: 10:30 - 11:30
Location: 861, Meyer Building
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Lecturer: Professor Rami Atar
Affiliations: The Andrew and Erna Viterbi Faculty of Electrical & Computer Engineering

Hydrodynamic limits of particle systems with selection are related to free boundary problems (FBP). The relation has been established in some cases; in others it is only formal, where the difficulty lies in questions of regularity of the free boundary and of the solution near it. We propose a weak formulation of a class of FBP that does not involve a free boundary at all, but is based instead on the heat (and other) equation(s) with measure-valued right-hand side. The approach avoids these regularity questions. In sharp contrast to existing methods, the PDE serves as a tool for proving hydrodynamic limits, and moreover provides new results in cases where classical solutions fail to exist.



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