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Andrei V. Faminskii

Publications and source records attributed to Andrei V. Faminskii.

10 recordsLinked to original sources
arXiv2025

Inverse problems with integral conditions for the generalized Korteweg-de Vries equation

Results on well-posedness of three inverse problems with integral conditions on a bounded interval for the generalized Korteweg-de Vries equation without any restrictions on the growth rate of nonlinearity are established. Either the right-hand side of equation or the boundary data, or both are chosen as controls. The considered solutions are regular with respect to the time variable. Assumptions on smallness of the input data or smallness of a time interval are required.

math.AP↗
arXiv2022

The higher order nonlinear Schrödinger equation with quadratic nonlinearity on the real axis

The initial value problem is considered for a higher order nonlinear Schrödinger equation with quadratic nonlinearity. Results on existence and uniqueness of weak solutions are obtained. In the case of an effective at infinity additional damping large-time decay of solutions without any smallness assumptions is also established. The main difficulty of the study is the non-smooth character of the nonlinearity.

math.AP↗
arXiv2022

Initial-Boundary Value Problems on a Half-Strip for the Generalized Kawahara-Zakharov-Kuznetsov Equation

Initial-boundary value problems on a half-strip with different types of boundary conditions for the generalized Kawahara-Zakharov-Kuznetsov equation with nonlinearity of higher order are considered. In particular, nonlinearity can be quadratic and cubic. Results on global existence and uniqueness in classes of weak and strong solutions and large-time decay of small solutions are established. The solutions are considered in weighted at infinity Sobolev spaces. The use of weighted spaces is crucial for the study. To this end new interpolating inequalities in weighted anisotropic Sobolev spaces are established. Both exponential and power weights are admissible.

math.AP↗
arXiv2017

Initial-boundary value problems in a rectangle for two-dimensional Zakharov-Kuznetsov equation

Initial-boundary value problems in a bounded rectangle with different types of boundary conditions for two-dimensional Zakharov-Kuznetsov equation are considered. Results on global well-posedness in the classes of weak and regular solution are established. As applications of the developed technique results on boundary controllability and long-time decay of weak solutions are also obtained.

math.AP↗
arXiv2014

An initial-boundary value problem in a strip for a two-dimensional equation of Zakharov-Kuznetsov type

An initial-boundary value problem in a strip with homogeneous Diriclet boundary conditions for two-dimensional generalized Zakharov-Kuznetsov equation is considered. In particular, dissipative and absorbing degenerate terms can be supplemented to the original Zakharov-Kuznetsov equation. Results on global existence, uniqueness and long-time decay of weak silutions are established.

math.AP↗