Universality of Crystallographic Pinning

Wednesday, December 5, 2012 - 10:15am - 11:05am
Keller 3-180
Aaron Hoffman (Franklin W. Olin College of Engineering)
We study traveling waves for bistable reaction diffusion equations on the spatially discrete domain rectangular lattice in two spatial dimensions. Pinning or propagation failure refers to the existence of a stationary planar front at parameter values for which the two spatially homogeneous stable equilibria are energetically distinct. This front blocks the invasion by the energetically favorable stable equilibrium of the spatial domain occupied by the less energetically favorable stable equilibrium. Crystallographic pinning refers to roughness in the strength of the pinning regarded as a function of the direction in the two-dimensional lattice which the stationary front faces. We give a generic condition under which crystallographic pinning is guaranteed to hold in the lattice directions. The proof is based on dynamical systems. This is joint work with J. Mallet-Paret.
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