IIMAS - FENOMEC
UNAM
Metastable dynamics for hyperbolic
variations of the Allen-Cahn equation
Resumen:
The phenomenon of metastability appears when the time
dependent solution of an evolution PDE, in a first phase,
evolves very slowly in time and after a very long time
undergoes a drastic change. We refer to this type of solutions
as metastable states for the evolution PDE. Such metastable
behavior was firstly observed for the Allen-Cahn equation,
that is a (parabolic) reaction-diffusion equation with a
balanced bistable reaction term, introduced to describe
transition processes. The aim of this talk is to extend the
metastable properties of the solutions to some hyperbolic
variations of the Allen-Cahn equation and study the
differences with the classic parabolic case. In particular,
after briefly recalling the classical results for the
Allen-Cahn equation, I will present the new results for the
hyperbolic Allen-Cahn equation, obtained by using two
different approaches.
Informes: coloquiomym@gmail.com, o al 5622-3564.