### Parabolic PDE's and deterministic games

Robert V. Kohn (Courant Institute, NYU)

We usually think of parabolic partial differential equations and
first-order Hamilton-Jacobi equations as being quite different. Parabolic
equations are linked to random walks, and often arise as
steepest-descents; Hamilton-Jacobi equations have characteristics, and
often arise from optimal control problems. In truth, these equations are
not so different. I will discuss recent work with Sylvia Serfaty, which
provides deterministic optimal-control interpretations of many parabolic
PDE. In some cases -- for example motion by curvature -- the optimal
control viewpoint is very natural, geometric, and easy to understand. In
other cases -- for example the linear heat equation -- it seems a bit less
natural, and therefore even more surprising.

#### Colloquium, Department of Mathematics, Rice University

October 18, 2007

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