Hyperbolic traveling fronts: the bistable equation with relaxation

The main concern of the talk is to discuss a class of hyperbolic equation
in the presence of a reaction term of Allen-Cahn type, motivated by
the assumption that the alignment of the flux term with the gradient of the unknown function is not istantaneous but delayed by the presence of a relaxation time.
After a brief overview on the derivation of such class of equations
starting from some appropriate modelling assumptions, emphasis will be given to the topic of front propagation in one dimension.
Rigorous results concerning existence and stability of planar fronts will be presented, comparing it with the corresponding results for the
standard parabolic Allen--Cahn equation.

(joint collaboration with C.Lattanzio, R.G.Plaza, C.Simeoni)