Regularity of the free boundary in Bernoulli-type problems
Abstract
I study free boundary problems with Bernoulli-type free boundary conditions. These types of problems naturally appear in the study of the propagation of flames in the high activation energy limit. In the first part, a divergence-form degenerate elliptic operator is studied and the regularity of the free boundary is established. In the second part, a more natural development for regularity of the free boundary in the Bernoulli-type problem associated with the heat equation is proven. Finally, the uniqueness of solutions to general parabolic free boundary problems with Bernoulli-type free boundary conditions is shown.
Degree
Ph.D.
Advisors
Danielli, Purdue University.
Subject Area
Applied Mathematics|Mathematics
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