On the spectral stability of traveling fronts for nonlinear reaction diffusion-degenerate equations

Motivated by biological applications (e.g. spatial ecology, bacterial
aggregation), several reaction-diffusion models consider density-dependent
diffusion coefficients which, in addition, are degenerate in one (or more)
equilibrium points of the reaction. These degenerate diffusion coefficients
describe, for example, the avoidance of crowded areas by individuals of
certain biological populations. In this talk, I shall present new results
and techniques in the study of stability of traveling fronts for reaction-
diffusion equations with degenerate diffusion. I will explain the two main
ideas to control, on one hand, the continuous spectrum and, on the other
hand, the point spectrum of the linearized operator around the front. Both
techniques are designed to overcome the degeneracy of the diffusion at one
of the end points. This is joint work with J. Francisco Leyva.