Abstract
We study a free boundary problem with initial data given on three-dimensional cones. In particular, we study when the free boundary is allowed to pass through the vertex of the cone, which depends on the cone’s slope, determined by a parameter c. With a mix of analytical and computational methods, we show that the free boundary may pass through the vertex of the cone when c ≤ 0.43.
Degree
MS
College and Department
Physical and Mathematical Sciences; Mathematics
Rights
https://lib.byu.edu/about/copyright/
BYU ScholarsArchive Citation
Zhao, Mingyan, "Minimizer of A Free Boundary Problem" (2021). Theses and Dissertations. 9356.
https://scholarsarchive.byu.edu/etd/9356
Date Submitted
2021-12-13
Document Type
Thesis
Handle
http://hdl.lib.byu.edu/1877/etd11993
Keywords
Free boundary problem, PDE, Legendre polynomial, computer-assisted method of proof
Language
english