5 papers · 1 filter
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…
Well-Posedness of the Nonlinear Schrödinger Equation on the Half-Plane
A. Alexandrou Himonas, Dionyssios Mantzavinos
The initial-boundary value problem (IBVP) for the nonlinear Schrödinger (NLS) equation on the half-plane with nonzero boundary data is studied by advancing a novel approach recentl…
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…
Ill-posedness results for generalized Boussinesq equations
Dan-Andrei Geba, A. Alexandrou Himonas, David Karapetyan
In this article we present ill-posedness results for generalized Boussinesq equations, which incorporate also the ones obtained by the authors for the classical "good" Boussinesq e…
Persistence Properties and Unique Continuation of solutions of the Camassa-Holm equation
A. Alexandrou Himonas, Gerard Misiołek, Gustavo Ponce +1
It is shown that a strong solution of the Camassa-Holm equation, initially decaying exponentially together with its spacial derivative, must be identically equal to zero if it also…