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Gradient flow structure for some nonlocal diffusion equations

Andrew Warren (University of British Columbia)
Monday, April 24, 2023 - 2:30pm to 3:30pm
ECE 026
I discuss some recent work regarding nonlocal diffusion equations
with a prescribed equilibrium state, which arise as the gradient flow of
the relative entropy with respect to a version of the nonlocal Wasserstein
metric introduced by Erbar. Such equations may also be viewed as the
evolutionary Gamma-limit of a certain sequence of heat flows on discrete
Markov chains. I will discuss criteria for existence, uniqueness, and
stability of solutions, and sufficient criteria on the equilibrium state
which ensure fast convergence to equilibrium.
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