Fast propagation for KPP equations with slowly decaying initial conditions. (English) Zbl 1213.35100
This paper concerns an analysis of the large-time behavior of solutions of one-dimensional Fisher-KPP reaction-diffusion equations. The initial conditions are assumed to be globally front-like and to decay at infinity towards the unstable steady state more slowly than any exponentially decaying function. The authors prove that all level sets of the solutions move infinitely fast as time goes to infinity. The locations of the level sets are expressed in terms of the decay of the initial condition. Furthermore, the spatial profiles of the solutions become asymptotically uniformly flat at large time.
Reviewer: Sebastian Anita (Iaşi)
MSC:
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35K57 | Reaction-diffusion equations |
| 35K58 | Semilinear parabolic equations |
| 35B35 | Stability in context of PDEs |
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