**UBC Mathematics Department**

*http://www.math.ubc.ca*

## Colloquium Abstract: Dr. Michael Ward, Department of Mathematics,
UBC

*Dynamic Metastability and Singular Perturbations*

Certain singularly perturbed partial differential equations exhibit
a phenomenon known as dynamic metastability, whereby reaction-diffusion
patterns evolve exponentially slowly in time. In particular, this
metastability occurs in the propagation of interfaces for phase
separation models, including the Cahn-Hilliard equation, with
applications to material science. Metastable behavior can also
occur in other physical settings including, the motion of a
flame-front in a vertical channel, the motion of spike solutions
for activator-inhibitor models from the theory of morphogenesis,
and the motion of hot-spots arising in the microwave heating of
ceramic materials. A common feature in many of these models is
that the underlying partial differential equation is of non-local
type and has asymptotically exponentially small eigenvalues. The
speaker will illustrate metastable behavior for a wide variety of
problems and show how asymptotic analysis can be used to quantify
the slow motion.

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