40 citations · 264 across the 35 of their papers we have counts for
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math.AP2011★ 1 cited
On the validity of formal asymptotic expansions in Allen-Cahn equation and FitzHugh-Nagumo system with generic initial data
Matthieu Alfaro, Hiroshi Matano
Formal asymptotic expansions have long been used to study the singularly perturbed Allen-Cahn type equations and reaction-diffusion systems, including in particular the FitzHugh-Na…
math.AP2011
Interface dynamics of the porous medium equation with a bistable reaction term
Matthieu Alfaro, Danielle Hilhorst
We consider a degenerate partial differential equation arising in population dynamics, namely the porous medium equation with a bistable reaction term. We study its asymptotic beha…
math.AP2011★ 1 cited
Convergence to a propagating front in a degenerate Fisher-KPP equation with advection
Matthieu Alfaro, Elisabeth Logak
We consider a Fisher-KPP equation with density-dependent diffusion and advection, arising from a chemotaxis-growth model. We study its behavior as a small parameter, related to the…