3 papers
math.AP2021
On the well-posedness of a nonlinear diffusive SIR epidemic model
C. Holliman, H. Prieto
This work considers an extension of the SIR equations from epidemiology that includes a spatial variable. This model, referred to as the Kermack-McKendrick equations (KM), is a pai…
math.AP2020
Well-posedness for a modified nonlinear Schrodinger equation modeling the formation of rogue waves
Curtis Holliman, Logan Hyslop
The Cauchy problem for a higher order modification of the nonlinear Shcrodinger equation (MNLS) on the line is shown to be well-posed in Sobolev spaces with exponent . This…
math.AP2017
Construction of 2-peakon Solutions and Ill-Posedness for the Novikov equation
A. Alexandrou Himonas, Curtis Holliman, Carlos Kenig
For the Novikov equation, on both the line and the circle, we construct a 2-peakon solution with an asymmetric antipeakon-peakon initial profile whose -norm for is arb…