3 papers
math.AP2024
Global solutions and Asymptotic Behavior to a Norm-preserving Non-local Parabolic Flow
Boris Shakarov
We consider a nonlinear parabolic model that forces solutions to stay on a -sphere through a nonlocal term in the equation. We study the local and global well-posedness on a b…
math.AP2024
Ground states on a fractured strip and one dimensional reduction
Stefan Le Coz, Boris Shakarov
We consider the nonlinear Schr\''odinger equation on a strip with Neumann boundary conditions and a delta condition on the -axis. First, we show the existence of ground states a…
math.AP2023
On the formation of singularities for the slightly supercritical NLS equation with nonlinear damping
Paolo Antonelli, Boris Shakarov
We consider the focusing, mass-supercritical NLS equation augmented with a nonlinear damping term. We provide sufficient conditions on the nonlinearity exponents and damping coeffi…