We consider an Allen-Cahn type equation of the form ut = ∆u + εf(x, t, u), where ε is a small parameter and f(x, t, u) = f(u) − εg(x, t, u) a bistable nonlinearity associated with a double-well potential whose well-depths can be slightly unbalanced. Given a rather general initial data u0 that is independent of ε, we perform a rigorous analysis of both the generation and the motion of interface....
