Front propagation for reaction-diffusion equations of bistable type

We present a direct PDE approach to study the behavior as ε → 0 of the solution uε of the reaction-diffusion equation: utε−εΔuε=(1/ε)f(uε) in ℝN × (0, ∞) in the case when f is the derivative of a bistable potential. Such singular perturbation problems arise in the study of large time wavefront propagations generated by such equations following a method introduced by M. Freidlin.