On absorbing set for 3D Maxwell--Schrödinger damped driven equations in bounded region

Abstract

We consider the 3D damped driven Maxwell-Schrödinger equations in a bounded region under suitable boundary conditions. We establish new a priori estimates, which provide the existence of global finite energy weak solutions and bounded absorbing set. The proofs rely on the Sobolev type estimates for magnetic Schrödinger operator.

On quantum jumps and attractors of the Maxwell–Schrödinger equations

“…We obtain the results for the Maxwell-Bloch equations which are finite-dimensional Galerkin approximation of the semiclassical Maxwell-Schrödinger system in a bounded cavity, see [1,9,14,16]. We prove the existence of time-periodic solutions for the equations reduced by the symmetry gauge group.…”

“…The Maxwell-Bloch equations are traditionally used for the semiclassical description of the laser action [10,13,24,26,27]. The equations are finite-dimensional approximation of the semiclassical Maxwell-Schrödinger system in a bounded cavity, see [1,9,14,16].…”