3 papers
math.AP2026
Spectral analysis of the classical Rayleigh-Taylor instability with an upper free surface
Blake Barker, Tien-Tai Nguyen, Benjamin Settle
In this note, we are interested in the linear Rayleigh-Taylor instability problem for the incompressible fluid with an upper free surface. Using the spectral theory of self-adjoint…
math.AP2026
Rate-Induced Tipping in a Non-Uniformly Moving Habitat and Determination of the Critical Rate
Blake Barker, Emmanuel Fleurantin, Matt Holzer +2
A habitat that is moving due to environmental change may result in tipping to extinction if the rate at which it moves is too great. We use a scalar reaction-diffusion equation wit…
math.AP2025
Asymptotic stability of sharp fronts: Analysis and rigorous computation
Blake Barker, Jared C. Bronski, Vera Mikyoung Hur +1
We investigate the stability of traveling front solutions to nonlinear diffusive-dispersive equations of Burgers type, with a primary focus on the Korteweg-de Vries-Burgers (KdVB)…