26 citations · 27 across the 5 of their papers we have counts for
6 papers
The nonlinear Schrödinger equation on the half-space
A. Alexandrou Himonas, Fangchi Yan
This work studies the initial-boundary value problem for both the linear Schrödinger equation and the cubic nonlinear Schrödinger equation on the half-space in higher dimensions ($…
Global solutions of quasi-linear Hamiltonian mKdV equation
Fangchi Yan, Qingtian Zhang
We study the initial value problem of quasi-linear Hamiltonian mKdV equations. Our goal is to prove the global-in-time existence of a solution given sufficiently smooth, localized,…
The Majda-Biello system on the half-line
A. Alexandrou Himonas, Fangchi Yan
The Majda-Biello system models the interaction of Rossby waves. It consists of two coupled KdV equations one of which has a parameter as coefficient of its dispersion. This wor…
A higher dispersion KdV equation on the half-line
A. Alexanddrou Himonas, Fangchi Yan
The initial-boundary value problem (ibvp) for the -th order dispersion Korteweg-de Vries (KdV) equation on the half-line with rough data and solution in restricted Bourgain spac…
Global solutions of quasi-geostrophic shallow-water fronts
Fangchi Yan, Qingtian Zhang
In this paper, we consider a family of piecewise constant solutions of the quasi-geostrophic shallow-water (QGSW) equation. We derive the contour dynamics equation of the QGSW fron…
Well-Posedness of Initial-Boundary Value Problems for a Reaction-Diffusion Equation
A. Alexandrou Himonas, Dionyssios Mantzavinos, Fangchi Yan
A reaction-diffusion equation with power nonlinearity formulated either on the half-line or on the finite interval with nonzero boundary conditions is shown to be locally well-pose…