PDE Seminar - Christopher Henderson

October 3, 2017
Tuesday, November 14, 2017 - 1:00pm to 2:00pm
Math Tower 154
Christopher Henderson

Title: A local-in-time Harnack inequality and applications to reaction-diffusion equations

SpeakerChristopher Henderson (University of Washington)

Abstract: The classical Harnack inequality requires one to look back in time to relate the suprema and infima of a solution to a parabolic equation. In this talk, I will introduce a Harnack-type inequality that allows us to remove this looking-back-in-time restriction at the expense of a slightly weaker bound. I will then discuss applications of this bound to (time permitting) three non-local reaction-diffusion equations arising in biology and combustion. In particular, in each case, this inequality allows us to show that solutions to these equations, which do not enjoy a maximum principle, may be compared with solutions to a related local equation, which does enjoy a maximum principle. Precise estimates of the propagation speed follow from this.

Seminar URLhttps://research.math.osu.edu/pde/

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