"Simplifying equations for a thin plate"
We will consider wave propagation through a thin plate, i.e. a solid
has one thin direction and two thick directions. This wave propagation is
governed by a partial differential equation (PDE) defined on three spatial
dimensions. We will focus on the question: When can we replace the 3D
equation(s) with a PDE defined on two spatial dimensions, and what will the
2D equations be?
If the plate is thin enough, we can make the replacement, and furthermore,
we will see that there is a hierarchy of 2D PDEs, each of which affords a
better approximation to the real equations. The viewpoint taken here is to
consider the dynamics on this plate as an infinite-dimensional dynamical
system of coupled oscillators.
The talk will not emphasize the technical aspects of the theory, and
intended to be accessible to all students who have had a class in ordinary