Date of Completion

7-25-2014

Embargo Period

7-25-2014

Keywords

Fractional Laplacian, s-Harmonic Extension, Traveling fronts, Existence

Major Advisor

Changfeng Gui

Associate Advisor

Yung-Sze Choi

Associate Advisor

Joseph McKenna

Field of Study

Mathematics

Degree

Doctor of Philosophy

Open Access

Open Access

Abstract

We consider the traveling fronts of the reaction diffusion equations with fractional Laplacian. We show the nonexistence of the traveling fronts in the combustion model with fractional Laplacian in the supercritical case. Our method can be used to give a direct and simple proof of the nonexistence of traveling fronts for the Fisher-KPP nonlinearity. Also we prove the existence and nonexistence of traveling fronts for different ranges of the fractional power in the generalized Fisher-KPP type model.

Download
COinS