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Advanced asymptotics of PDEs and applications

course: Spikes and vortices in inhomogeneous environments

speaker: Theodore Kolokolnikov (Dalhousie University)

abstract: I will discuss spike distribution in reaction-diffusion systems with space-dependent parameters. This involves two levels of reduction: first, we use by-now standard asymptotic techniques to derive a system of reduced equations for spike centers and height. Second, we take a continuum limit of the reduced system, resulting in novel system of nonlocal PDE's. Finally the resulting PDE's are solved asymptotically to yield an effective description of spike density. As a bonus, we obtain instability thresholds for N spikes in one dimension. We also generalize these results in two dimensions. Several open questions will also be presented.

timetable:
Thu 27 Sep, 10:00 - 11:05, Aula Dini
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