336 citations · 997 across the 39 of their papers we have counts for
41 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…
The Evans function as a lower bound on the spectral distance function
George Bayliss, Jared C. Bronski
The Evans function is an analytic function that encodes information about the intersection of certain subspaces in ODE boundary value problems. As such it is a useful tool for comp…
Cycle intersection form and oscillation of graph eigenfunctions
Gregory Berkolaiko, Jared C. Bronski, Mark Goresky
For a real symmetric matrix strictly supported on a finite simple graph, it is shown that the inertia of a weighted intersection form on the cycle space of the graph, with weig…
Bounds on unstable spectrum for dispersive Hamiltonian PDEs
Jared C Bronski, Ver Mikyoung Hur, Sarah E Simpson
We study quasi-periodic eigenvalue problems that arise in the stability analysis of periodic traveling wave solutions to Hamiltonian PDEs. We establish bounds on regions in the com…
Floquet theory and stability for Hamiltonian partial differential equations
Jared C Bronski, Vera Mikyoung Hur, Robert Marangell
We analyze Floquet theory as it applies to the stability and instability of periodic traveling waves in Hamiltonian PDEs. Our investigation focuses on several examples of such PDEs…
Correlation function of a random scalar field evolving with a rapidly fluctuating Gaussian process
Jared C. Bronski, Lingyun Ding, Richard M. McLaughlin
We consider a scalar field governed by an advection-diffusion equation (or a more general evolution equation) with rapidly fluctuating, Gaussian distributed random coefficients. In…