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math.AP2019★ 8 cited
Quantitative estimates of the threshold phenomena for propagation in reaction-diffusion equations
Matthieu Alfaro, Arnaud Ducrot, Gregory Faye
We focus on the (sharp) threshold phenomena arising in some reaction-diffusion equations supplemented with some compactly supported initial data. In the so-called ignition and bist…
math.AP2019
Asymptotic stability of the critical pulled front in a Lotka-Volterra competition model
Gregory Faye, Matt Holzer
We prove that the critical pulled front of Lotka-Volterra competition systems is nonlinearly asymptotically stable. More precisely, we show that perturbations of the critical front…