Seminar in Applied Mathematics

Amitabha Bose Department of Mathematical Sciences New Jersey Institute of Technology Non-local Reaction-diffusion Equations for Microwave Heating Applications Monday, March 6, 2000 3:00pm Pierce 116

Abstract:   Motivated by recent microwave heating experiments on ceramic fibers in single-mode cavities, we present a new geometric approach to establishing the existence and stability of large pulse solutions of non-local reaction diffusion equations. Existence of solutions is determined by showing that the pulses lie in the transverse intersection of relevant invariant manifolds. The transverse intersection encodes a consistency condition that all non-local equations must satisfy. Stability is determined by locating the spectrum of a non-local Sturm-Liouville operator. The results apply to both spatially homogeneous and non-homogeneous equations. We discuss how the stability of the solutions depends critically on the spatial non-homogeneities.

Coffee and refreshments will be available starting at 3:00pm. For additional information contact Patrick Miller  or Yi Li.