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Home » Postdoc Symposium (Part II): Front Propagation and Symmetrization in the Nonlocal Fisher-KPP Equation

Seminar

Postdoc Symposium (Part II): Front Propagation and Symmetrization in the Nonlocal Fisher-KPP Equation November 20, 2015 (01:15 PM PST - 02:00 PM PST)
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Location: MSRI: Simons Auditorium
Speaker(s) Andrei Tarfulea (University of Chicago)
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We prove strong gradient decay estimates for solutions to the multi-dimensional Fisher-KPP equation with fractional diffusion. It is known that this equation exhibits exponentially advancing level sets with strong qualitative upper and lower bounds on the solution. However, little has been shown concerning the gradient of the solution. We prove that, under mild conditions on the initial data, the first and second derivatives of the solution obey a comparative exponential decay in time. We then use this estimate to prove a symmetrization result, which shows that the reaction front circularizes in renormalized coordinates.

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