相关论文: Initial-Boundary Value Problems on a Half-Strip fo…
Initial-boundary value problems in a half-strip with different types of boundary conditions for two-dimensional Zakharov-Kuznetsov equation are considered. Results on global existence, uniqueness and long-time decay of weak and regular…
Initial-boundary value problems in a strip with different types of boundary conditions for two-dimensional generalized Zakharov--Kuznetsov equation are considered. Results on global existence and uniqueness of weak solutions in certain…
Initial-boundary value problems in a half-strip with different types of boundary conditions for two-dimensional Zakharov-Kuznetsov equation are considered. Results on global well-posedness in classes of regular solutions in the cases of…
An initial-boundary value problem for the critical generalized 2D Zakharov-Kuznetsov equation posed on a half-strip is considered. Existence, uniqueness and the exponential decay rate of global regular solutions for small initial data are…
An initial-boundary value problem for the generalized 2D Zakharov-Kuznetsov equation posed on the right half-strip is considered. Existence, uniqueness and the exponential decay rate of global regular solutions for small initial data are…
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…
An initial-boundary value problem with homogeneous Dirichlet boundary conditions for three-dimensional Zakharov-Kuznetsov equation is considered. Results on global existence, uniqueness and large-time decay of weak solutions in certain…
An initial-boundary value in a strip with homogeneous Dirichlet boundary conditions for two-dimensional Zakharov-Kuznetsov-Burgers equation is considered. Results on global well-posedness and long-time decay of solutions in Sobolev spaces…
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…
Initial-boundary value problem for the generalized Zakharov-Kuznetsov equation posed on a bounded rectangle is considered. Critical and subcritical powers in nonlinearity are studied.
In this work we consider the initial value problem (IVP) associated to the two dimensional Zakharov-Kuznetsov equation $$\left. \begin{array}{rl} u_t+\partial_x^3 u+\partial_x \partial_y^2 u +u \partial_x u &\hspace{-2mm}=0,\qquad\qquad…
Initial-boundary value problems for the 2D Zakharov-Kuznetsov equation posed on bounded rectangles and on a strip are considered. Spectral properties of a linearized operator and critical sizes of domains are studied. Exponential decay of…
We study the initial boundary value problem for one-dimensional Kuramoto-Sivashinsky equation with nonhomogeneous boundary conditions. Through the analysis of the boundary integral operator, and applying the known results on the Cauchy…
We formulate on a half-strip an initial boundary value problem for the two-dmensional Kawahara equation. Existence and uniqueness of a regular solution as well as the exponential decay rate for the elevated norm of small solutions are…
Initial-boundary value problem for the modified Zakharov-Kuznetsov equation posed on a bounded rectangle is considered. The main difficulty is the critical power in nonlinear term. The results on existence, uniqueness and asymptotic…
An initial-boundary value problem for the 2D Zakharov-Kuznetsov-Burgers equation posed on a channel-type strip was considered. The existence and uniqueness results for regular and weak solutions in weighted spaces as well as exponential…
We study the initial-boundary value problem of the stochastic Navier--Stokes equations in the half space. We prove the existence of weak solutions in the standard Besov space valued random processes when the initial data belong to the…
An initial-boundary value problem for the 3D Zakharov-Kuznetsov equation posed on an unbounded domain is considered. Existence and uniqueness of a global regular solution as well as exponential decay of the $H^2$-norm for small initial data…
An initial-boundary value problem with one boundary condition is considered for the higher order nonlinear Schr\"odinger equation. It is assumed that either the boundary condition is homogeneous or the nonlinearity in the equation is…
We consider the so-called Gross-Pitaevskii equations supplemented with non-standard boundary conditions. We prove two mathematical results concerned with the initial value problem for these equations in Zhidkov spaces.