Convergence to pushed fronts

Abstract

We study the convergence to the stationary state for the parabolic equation ut = uxx + f(0) with f′(0) > 0 in case there exist front-type solutions U(x + ct) for a continuum of velocities c ≥ c(f) and c2(f) > c2f′(0). The initial data are only restricted in their asymptotic behavior for x→∞. We prove strict uniform convergence to a front with velocity c(f) (or a pair of diverging fronts, respectively) with an exponential rate. © 1981 Rocky Mountain Mathematical Consortium.