Ohio State nav bar

PDE Seminar - Christopher Henderson

Christopher Henderson
November 14, 2017
1:00PM - 2:00PM
Math Tower 154

Date Range
Add to Calendar 2017-11-14 13:00:00 2017-11-14 14:00:00 PDE Seminar - Christopher Henderson Title: A local-in-time Harnack inequality and applications to reaction-diffusion equationsSpeaker: Christopher 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 URL: https://research.math.osu.edu/pde/ Math Tower 154 Department of Mathematics math@osu.edu America/New_York public

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/

Events Filters: