176 citations · 768 across the 86 of their papers we have counts for
6 papers · 2 filters
Pointwise dispersive estimates for Schrödinger operators on product cones
Blake Keeler, Jeremy L. Marzuola
We investigate the dispersive properties of solutions to the Schrödinger equation with a weakly decaying radial potential on cones. If the potential has sufficient polynomial decay…
Defect resonances of truncated crystal structures
Jianfeng Lu, Jeremy L. Marzuola, Alexander B. Watson
Defects in the atomic structure of crystalline materials may spawn electronic bound states, known as \emph{defect states}, which decay rapidly away from the defect. Simplified mode…
The essential spectrum of periodically-stationary solutions of the complex Ginzburg-Landau equation
John Zweck, Yuri Latushkin, Jeremy L. Marzuola +1
We establish the existence and regularity properties of a monodromy operator for the linearization of the cubic-quintic complex Ginzburg-Landau equation about a periodically-statio…
Local well-posedness for a quasilinear Schrödinger equation with degenerate dispersion
Benjamin Harrop-Griffiths, Jeremy L. Marzuola
We consider a quasilinear Schrödinger equation on for which the dispersive effects degenerate when the solution vanishes. We first prove local well-posedness for suffic…
Analysis of a fourth order exponential PDE arising from a crystal surface jump process with Metropolis-type transition rates
Yuan Gao, Anya E. Katsevich, Jian-Guo Liu +2
We analytically and numerically study a fourth order PDE modeling rough crystal surface diffusion on the macroscopic level. We discuss existence of solutions globally in time and l…
Quasilinear Schrödinger equations III: Large Data and Short Time
Jeremy L. Marzuola, Jason Metcalfe, Daniel Tataru
In this article we prove short time local well-posedness in low-regularity Sobolev spaces for large data general quasilinear Schrödinger equations with a non-trapping assumption. T…