Zobrazeno 1 - 10
of 38
pro vyhledávání: '"Avery, Montie"'
Autor:
Avery, Montie
We study growth of solid tumors in a partial differential equation model introduced by Hillen et al for the interaction between tumor cells (TCs) and cancer stem cells (CSCs). We find that invasion into the cancer-free state may be separated into two
Externí odkaz:
http://arxiv.org/abs/2310.17633
Autor:
Avery, Montie
We describe the resulting spatiotemporal dynamics when a homogeneous equilibrium loses stability in a spatially extended system. More precisely, we consider reaction-diffusion systems, assuming only that the reaction kinetics undergo a transcritical,
Externí odkaz:
http://arxiv.org/abs/2310.13602
We establish sharp nonlinear stability results for fronts that describe the creation of a periodic pattern through the invasion of an unstable state. The fronts we consider are critical, in the sense that they are expected to mediate pattern selectio
Externí odkaz:
http://arxiv.org/abs/2310.08765
Motivated by the impact of worsening climate conditions on vegetation patches, we study dynamic instabilities in an idealized Ginzburg-Landau model. Our main results predict time instances of sudden drops in wavenumber and the resulting target states
Externí odkaz:
http://arxiv.org/abs/2309.14959
We analyze spatial spreading in a population model with logistic growth and chemorepulsion. In a parameter range of short-range chemo-diffusion, we use geometric singular perturbation theory and functional-analytic farfield-core decompositions to ide
Externí odkaz:
http://arxiv.org/abs/2308.01754
Autor:
Avery, Montie
We show that propagation speeds in invasion processes modeled by reaction-diffusion systems are determined by marginal spectral stability conditions, as predicted by the marginal stability conjecture. This conjecture was recently settled in scalar eq
Externí odkaz:
http://arxiv.org/abs/2211.11829
We analyze the transition between pulled and pushed fronts both analytically and numerically from a model-independent perspective. Based on minimal conceptual assumptions, we show that pushed fronts bifurcate from a branch of pulled fronts with an ef
Externí odkaz:
http://arxiv.org/abs/2206.09989
Autor:
Avery, Montie, Scheel, Arnd
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 rate $t^{-3/2}$, while the phase decays diffusively. We thereby refine
Externí odkaz:
http://arxiv.org/abs/2103.10458
Autor:
Avery, Montie, Scheel, Arnd
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, including one-sided compactly supported initial conditions. We rely o
Externí odkaz:
http://arxiv.org/abs/2012.06443
Autor:
Avery, Montie, Scheel, Arnd
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 fronts. In this general setting, we establish sharp algebraic decay r
Externí odkaz:
http://arxiv.org/abs/2012.02722