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math.AP2024
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 ($…
math.AP2022
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…
math.AP2018
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…