arXiv subjects
Publications and source records attributed to Nikolai A. Larkin.
Boundary value problems for linear stationary dispersive equations of order $2l+1$, $l\in \mathbb{N}$ have been considered on finite intervals $(0,L)$. The existence and uniqueness of regular solutions have been established for general linear boundary conditions.
Initial-boundary value problems for nonlinear dispersive equations of evolution of order $2l+1,\;l\in\mathbb{N}$ with a convective term of the form $u^ku_x,\;k\in\mathbb{N}$ have been considered on intervals $(0,L),\;L\in (0,+\infty)$. The existence and uniqueness of local regular solutions have been established.
A boundary value problem for a stationary nonlinear dispersive equation of order $2l+1\;\; l\in \mathbb{N}$ with a convective term in the form $u^ku_x\;\; k\in \mathbb{N}$ was considered on an interval $(0,L)$. The existence, uniqueness and continuous dependence of a regular solution as well as a relation between $l$ and critical values of $k$ have been established.
Initial-boundary value problems for the linear Zakharov-Kuznetsov equation posed on bounded rectangles are considered. Spectral properties of a stationary operator are studied in order to show that the evolution problem posed on a bounded rectangle has no critical restrictions on its size. Exponential decay of regular solutions is established.