Date of Completion
6-24-2014
Embargo Period
6-24-2014
Keywords
Traveling wave solution; Traveling speed; Allen–Cahn equation; Fractional Laplacian; Continuation method; Hamiltonian identity
Major Advisor
Changfeng Gui
Associate Advisor
Yung-Sze Choi
Associate Advisor
Xiaodong Yan
Field of Study
Mathematics
Degree
Doctor of Philosophy
Open Access
Open Access
Abstract
We show the existence of traveling wave solutions to the Allen-Cahn equation with fractional Laplacians. A key ingredient is the estimation of the traveling speed of traveling wave solutions. In the meantime, we prove some qualitative properties of the solution, e.g., monotonicity, polynomial decays at infinity, Hamiltonian identity and Modica type estimates, and non-degeneracy. Moreover, we prove that for any balanced bistable nonlinearity, the traveling speeds linearly depend on the perturbation parameters.
Recommended Citation
Zhao, Mingfeng, "Traveling Wave Solutions To The Allen-Cahn Equations With Fractional Laplacians" (2014). Doctoral Dissertations. 420.
https://digitalcommons.lib.uconn.edu/dissertations/420