A Fast Diffusion Equation

Open Access
Author:
Baisley, Sarah
Area of Honors:
Mathematics
Degree:
Bachelor of Science
Document Type:
Thesis
Thesis Supervisors:
  • Jeffrey Steven Case, Thesis Supervisor
  • Luen-Chau Li, Honors Advisor
Keywords:
  • Fast diffusion equation
  • stereographic projection
  • Hardy-Littlewood Sobolev Inequality
  • Gagliardo-Nirenberg-Sobolev Inequality
Abstract:
The fast diffusion equation is u_t=-Δu^β some 0 <β < 1. There is a conformally invariant analogue of the fast diffusion equation which has an interesting relationship to sharp Gagliardo–Nirenberg inequalities. This project involves carrying out a detailed study of this flow on the round spheres as a first step towards understanding the behavior of the flow on general manifolds.