Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

Convergence to travelling fronts in semilinear parabolic equations

Franz Rothea1

a1 Lehrstuhl für Biomathematik, Universität Tubingen

Synopsis

We study the convergence to the stationary state for the parabolic equation u, = uxx + F(u). There exist wave-type solutions u(x, t) = φ(xct) for a continuum of velocities c. In the asymptotic behavior of this equation was investigated for a step function as initial data. In this paper we obtain the asymptotic behavior for a large class of monotone initial data.

All solutions with initial data in this class evolve to wave-type solutions, where the rate of decay of the initial data determines the asymptotic speed.

(Received February 14 1977)

(Received February 17 1977)