Thin domains with a highly oscillating boundary

PDE Seminar
Tuesday, December 1, 2009 - 3:01pm for 1 hour (actually 50 minutes)
Skiles 255
Jose Arrieta – Universidad Complutense de Madrid; visiting faculty at GT
Maria Westdickenberg
In this talk we will present several results concerning the behavior of the Laplace operator with Neumann boundary conditions in a thin domain where its boundary presents a highly oscillatory behavior. Using homogenization and domain perturbation techniques, we obtain the asymptotic limit as the thickness of the domain goes to zero even for the case where the oscillations are not necessarily periodic. We will also indicate how this result can be applied to analyze the asymptotic dynamics of reaction diffusion equations in these domains.