4 papers
Global asymptotic stability of KdV-Burgers fronts in a weakly two-dimensional model
Jared C. Bronski, Olivia Clifton, Vera Mikyoung Hur
We study front-type solutions of nonlinear dispersive-dissipative PDEs modeling the propagation of undular bores in a channel in two dimensions. The system extends the Korteweg-de…
Kernel-Dependent Pattern Formation in a Population Model with Nonlocal Facilitation and Competition
Olivia Clifton, Stephanie Dodson, Daniel B. Cooney
Spatial patterns, such as those in dryland vegetation models, have historically been studied in systems of reaction-diffusion systems with pattern onset via a Turing bifurcation fr…
Vacuum bubble and fissure formation in collective motion with competing attractive and repulsive forces
Olivia Clifton, Angel Chavez, Antonio Madrigal +3
We study the continuum limit of the motion of agents in the plane driven by competing short-range repulsion and long-range attractive forces. At a critical parameter value, we find…
Coherent structures in nonlocal systems -- functional analytic tools
Olivia Cannon, Arnd Scheel
We develop tools for the analysis of fronts, pulses, and wave trains in spatially extended systems with nonlocal coupling. We first determine Fredholm properties of linear operator…