Aleksey . Shcherbina
Phd in mathematics, senior lecturer
List of selected publications
Igor D Chueshov, Aleksey S Shcherbina On 2D Zakharov system in a bounded domain // Differential and Integral Equations, v. 18, 2005, p.781-812,
The paper deals with initial boundary-value problems for the Zakharov system arising in plasma physics in two-dimensional domains under various boundary conditions. We prove the global well-posedness of these problems in some Sobolev-type classes and study properties of the solutions. In the dissipative case the existence of a global attractor is established.
Igor Chueshov, Alexey Shcherbina SEMI-WEAK WELL-POSEDNESS AND ATTRACTORS FOR 2D SCHRÖDINGER-BOUSSINESQ EQUATIONS. // Evolution Equations & Control Theory, v. 1, 2012,
We deal with an initial boundary value problem for the Schrödinger-Boussinesq system arising in plasma physics in two-dimensional domains. We prove the global Hadamard well-posedness of this problem (with respect to the topology which is weaker than topology associated with the standard variational (weak) solutions) and study properties of the solutions. In the dissipative case the existence of a global attractor is established.
A S Shcherbina The Singular Limit of the Dissipative Zakharov System // Journal of Mathematical Physics, Analysis, Geometry, V 11, No 1, p. 75-99, 2015,
The dissipative Zakharov system which models the propagation of Langmuir waves in plasmas is considered on the interval [0, L]. We are interested in the case of large ion acoustic speed λ. After the formal limiting transition λ → ∞ this system turns into the coupling system of the parabolic and Schrödinger equations. We prove that this limit system has a solution and generates a dissipative dynamical system possessing a global compact attractor. Our main result is the upper semicontinuity of the attractor as λ → ∞.
