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Applied Mathematics Colloquium: Dr Gautam Iyer

Carnegie Mellon University

Friday, October 29, 2021
2:00 PM – 3:00 PM
Dissipation Enhancement, Mixing and Blow-up Suppression

Diffusion and mixing are two fundamental phenomena that arise in a wide
variety of applications. In this talk we quantitatively study the
interaction between diffusion and mixing in the context of problems
arising in fluid dynamics. The first question we address is how fast the
energy can decay in the advection diffusion equation. Even though this
is a simple linear equation, the energy decay rate is intrinsically
related to the mixing properties of the advecting velocity field, and
there are many unresolved open questions. I will present a few recent
results involving both upper and lower bounds, and then consider
applications to studying the long time dynamics of a few model
non-linear equations arising in chemotaxis and phase separation.
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