40 citations · 264 across the 35 of their papers we have counts for
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math.AP2017
Interplay of nonlinear diffusion, initial tails and Allee effect on the speed of invasions
Matthieu Alfaro, Thomas Giletti
We focus on the spreading properties of solutions of monostable equations with non-linear diffusion. We consider both the porous medium diffusion and the fast diffusion regimes. In…
math.AP2017★ 29 cited
Superexponential growth or decay in the heat equation with a logarithmic nonlinearity
Matthieu Alfaro, Rémi Carles
We consider the heat equation with a logarithmic nonlinearity, on thereal line. For a suitable sign in front of the nonlinearity, weestablish the existence and uniqueness of soluti…
math.AP2017★ 22 cited
Travelling waves for a non-monotone bistable equation with delay: existence and oscillations
Matthieu Alfaro, Arnaud Ducrot, Thomas Giletti
We consider a bistable ($0\textless{}θ\textless{}1$ being the three constant steady states) delayed reaction diffusion equation, which serves as a model in population dynamics. The…