Seminar:
Analysis
Event time:
Thursday, April 14, 2022 - 4:15pm
Speaker:
Chris Henderson
Speaker affiliation:
University of Arizona
Event description:
In many systems, such as the invasion of a new species or turbulent combustion, a balance of growth (reaction) and spreading (diffusion) creates a moving interface called a front. The basic reaction-diffusion equations modeling these systems date back almost a century and their investigation is centered around the construction of traveling wave solutions and an analysis of their stability. The stability proofs are often inflexible (ad hoc to the particular model) and either non-quantitative or extremely intricate. In this talk, I will introduce a new ingredient, the shape defect function, that yields a simple, general framework to obtain and quantify stability of the traveling waves for a huge range of models, including both new and classical models.