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Front propagation into unstable states: Universal algebraic convergence towards uniformly translating pulled fronts. (English) Zbl 0984.35030
The authors analyze the convergence of asymptotically uniformly traveling pulled fronts toward their asymptotic speed $V^*$. It is shown that when such fronts evolve from “sufficiently steep” initial conditions (initial decay faster than $e^{-\lambda^*x}$ for $x\to\infty)$, then they have a universal relaxation behaviour as $t\to\infty$, i.e., the velocity of the pulled front relaxes algebraically like $$V(t)=V^* -{3\over 2\lambda^*t} +{3\over 2} \sqrt nD\lambda^*/ (D\lambda^{*2}t)^{3/2} +O(1/t^2).$$

MSC:
35B40Asymptotic behavior of solutions of PDE
35K57Reaction-diffusion equations
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