UBC Mathematics Department

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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