Asymptotics of a reaction-diffusion equation, driven by the fractional Laplacian

Inspired by some models arising in crystal dislocation,
we consider an evolution equation driven by
the fractional Laplacian with a small stress that is close
to constant in space and time.
We show that the solution, in the suitable space and time scale,
may be seen as the superposition of a finite
number of transition layers.
Each transition is centered at a point
that evolves by following the external stress and
subject to a repulsive potential
of fractional type.

Posted on Aug 9, 2013 in Differential Equations, Seminars