12:00 pm Friday, October 9, 2015
Junior Analysis: Blowups of Reaction-Diffusion Equations by Tim Carson in RLM 11.176
Under basic assumptions on the initial data, running the heat equation makes a function milder and milder. This is called diffusion; when the function is sharp, the laplacian pushes to smooth it out. If the ODE is allowed to do its thing, will go to infinity in finite time. This is called reaction; as the function gets larger the force pushing it to infinity gets larger as well. When both of these forces are in play at the same time, we have what is called a reaction-diffusion equation, and your domain may become a battlefield for an epic struggle between these forces. In this talk we will see either the reaction or diffusion terms winning battles. This is done through lens of a few theorems about the set where the solution goes to infinity, or the asymptotic shape of the solution as it goes to infinity. Submitted by
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