48 citations · 245 across the 41 of their papers we have counts for
19 papers · 1 filter
On dispersive estimates for one-dimensional Klein-Gordon equations
Elena Kopylova
We improve previous results on dispersive decay for 1D Klein- Gordon equation. We develop a novel approach, which allows us to establish the decay in more strong norms and weaken t…
Attractors of Hamiltonian nonlinear partial differential equations
Andrew Comech, Alexander Komech, Elena Kopylova
We survey the theory of attractors of nonlinear Hamiltonian partial differential equations since its appearance in 1990. These are results on global attraction to stationary states…
On spectral and orbital stability for the Klein--Gordon equation coupled to an anharmonic oscillator
Andrew Comech, Elena A. Kopylova
We obtain explicit characterization of spectral and orbital stability of solitary wave solutions to the -invariant Klein--Gordon equation in one spatial dimension co…
On global attractors for 2D damped driven nonlinear Schrödinger equations
A. Komech, E. Kopylova
Well-posedness and global attractor are established for 2D damped driven nonlinear Schrödinger equation with almost periodic pumping in a bounded region. The key role is played by…
Global well-posedness for Dirac equation with concentrated nonlinearity
Elena Kopylova
We prove global well-posedness for 3D Dirac equation with a concentrated nonlinearity.
On stability of ground states for finite crystals in the Schroedinger-Poisson model
Alexander Komech, Elena Kopylova
We consider the Schrödinger-Poisson-Newton equations for finite crystals under periodic boundary conditions with one ion per cell of a lattice. The electrons are described by one-p…