Abstract
SynopsisWe study the convergence to the stationary state for the parabolic equation u, = uxx + F(u). There exist wave-type solutions u(x, t) = φ(x − ct) 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.
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