Jonathan Bennett (Birmingham)
Generating monotone quantities for the heat equation
The identification of functionals which vary monotonically as their inputs
flow according to a given evolution equation is generally considered
to be more of an art than a science. Such monotonicity results have many
consequences and, in particular, allow for a deeper understanding of a variety
of important inequalities in analysis (via the so-called "semigroup method" or "semigroup interpolation").
The purpose of this talk is to describe a simple
framework within which a rich variety of monotone quantities for the heat equation on
R^n may be "generated".