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.
College and Department
Physical and Mathematical Sciences; Mathematics
BYU ScholarsArchive Citation
Zhao, Mingyan, "Minimizer of A Free Boundary Problem" (2021). Theses and Dissertations. 9356.
Free boundary problem, PDE, Legendre polynomial, computer-assisted method of proof