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20102023
most citedExistence and convergence to a propagating terrace in one-dimensional reaction-diffusion equations

4 citations · 4 across the 6 of their papers we have counts for

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math.AP2012★ 4 cited

Existence and convergence to a propagating terrace in one-dimensional reaction-diffusion equations

Arnaud Ducrot, Thomas Giletti, Hiroshi Matano

We consider one-dimensional reaction-diffusion equations for a large class of spatially periodic nonlinearities (including multistable ones) and study the asymptotic behavior of so…

math.AP2010

Sharp interface limit of the Fisher-KPP equation when initial data have slow exponential decay

Matthieu Alfaro, Arnaud Ducrot

We investigate the singular limit, as $\ep \to 0$, of the Fisher equation $\partial_t u=\ep Δu + \ep ^{-1}u(1-u)$ in the whole space. We consider initial data with compact support…