Convergence to traveling waves for time-periodic bistable reaction-diffusion equations.

We consider the equation u t = u xx + ƒ(t,u), x ∈ R, t > 0, where ƒ(t,x) periodically depends on t and is of bistable type. Classical results showed that for a large class of initial functions, the solutions converge to a periodic traveling wave if it connects two linearly stable time-periodic states. Under some conditions on the initial functions, we prove this convergence result by a new approach which allows the time-periodic states to be degenerate. [ABSTRACT FROM AUTHOR]

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