49 citations · 253 across the 59 of their papers we have counts for
6 papers · 1 filter
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…
Universal selection of pulled fronts
Montie Avery, Arnd Scheel
We establish selection of critical pulled fronts in invasion processes. Our result shows convergence to a pulled front with a logarithmic shift for open sets of steep initial data,…
Invasion into remnant instability: a case study of front dynamics
Gregory Faye, Matt Holzer, Arnd Scheel +1
We study the invasion of an unstable state by a propagating front in a peculiar but generic situation where the invasion process exhibits a remnant instability. Here, remnant insta…
Instability in large bounded domains -- branched versus unbranched resonances
Montie Avery, Cedric Dedina, Aislinn Smith +1
We study transitions from convective to absolute instability near a trivial state in large bounded domains for prototypical model problems in the presence of transport and negative…
Corrigendum to "Center Manifolds without a Phase Space"
Gregory Faye, Arnd Scheel
We correct the choice of cut-off function in our construction of center manifolds in [G. Faye and A. Scheel, \textit{Trans. Amer. Math. Soc.}, 370 (2018), pp. 5843--5885]. The main…
Spiral waves: linear and nonlinear theory
Björn Sandstede, Arnd Scheel
Spiral waves are striking self-organized coherent structures that organize spatio-temporal dynamics in dissipative, spatially extended systems. In this paper, we provide a conceptu…