4 papers
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…
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…
Growing stripes, with and without wrinkles
M. Avery, R. Goh, O. Goodloe +2
We present results on stripe formation in the Swift-Hohenberg equation with a directional quenching term. Stripes are "grown" in the wake of a moving parameter step line, and we an…
Pinning and Depinning: from periodic to chaotic and random media
Noah Ankney, Montie Avery, Tali Khain +1
We study propagation of dissipative structures in inhomogeneous media with a focus on pinning and depinning transitions. We model spatial complexity in the medium as generated by d…