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math.AP2021
Sharp decay rates for localized perturbations to the critical front in the Ginzburg-Landau equation
Montie Avery, Arnd Scheel
We revisit the nonlinear stability of the critical invasion front in the Ginzburg-Landau equation. Our main result shows that the amplitude of localized perturbations decays with r…
math.AP2020
Asymptotic stability of critical pulled fronts via resolvent expansions near the essential spectrum
Montie Avery, Arnd Scheel
We study nonlinear stability of pulled fronts in scalar parabolic equations on the real line of arbitrary order, under conceptual assumptions on existence and spectral stability of…
math.AP2019
Evolution of Interfaces for the Nonlinear Double Degenerate Parabolic Equation of Turbulent Filtration with Absorption. II. Fast Diffusion Case
Ugur G. Abdulla, Adam Prinkey, Montie Avery
We prove the short-time asymptotic formula for the interfaces and local solutions near the interfaces for the nonlinear double degenerate reaction-diffusion equation of turbulent f…