Related papers: Initial-boundary value problems in a half-strip fo…

The dynamical boundary value problem for viscoelastic half-space with cut in the form of a strip is considered. The problem is reduced to the singular integral equation of first kind. Using the method of orthogonal polynomials, the integral…

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.

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…

We consider the Zakharov-Kuznestov (ZK) equation posed in a limited domain (0,1)_{x}\times(-\pi /2, \pi /2)^d, d=1,2 supplemented with suitable boundary conditions. We prove that there exists a solution u \in \mathcal C ([0, T]; H^1(\dom))…

While there exist now formulations of initial boundary value problems for Einstein's field equations which are well posed and preserve constraints and gauge conditions, the question of geometric uniqueness remains unresolved. For two…

An initial-boundary value problem for a generalized KdV equation posed on a half-line is considered. Existence and uniqueness of global regular solutions for arbitrary smooth initial data are established.

This paper focuses on the initial- and boundary-value problem for the two-dimensional micropolar equations with only angular velocity dissipation in a smooth bounded domain. The aim here is to establish the global existence and uniqueness…

Initial boundary value problem on a half-line for the Modified KdV equation is considered with the boundary conditions equal to zero at the origin and initial condition chosen arbitrary decreasing rapidly enough and this problem is plunged…

Two important cases, where boundary conditions and solutions of the well-known integrable equations on a semi-strip are uniquely determined by the initial conditions, are rigorously studied in detail. First, the case of rectangular matrix…

We prove existence and uniqueness of solutions to the initial-boundary value problem for the Lifshitz--Slyozov equation (a nonlinear transport equation on the half-line), focusing on the case of kinetic rates with unbounded derivative at…

An initial-boundary value problem for the n-dimensional ($n$ is a natural number from the interval [2,7]) Kuramoto-Sivashinsky-Zakharov-Kuznetsov equation posed on smooth bounded domains in $\mathbb{R}^n$ was considered. The existence and…

In this paper we study the initial-value problem associated with the Benjamin-Ono-Zakharov-Kuznetsov equation. Such equation appears as a two-dimensional generalization of the Benjamin-Ono equation when transverse effects are included via…

We examine initial-boundary value problems for diffusion equations with distributed order time-fractional derivatives. We prove existence and uniqueness results for the weak solution to these systems, together with its continuous dependency…

This paper studies an initial boundary value problem for a class of nonlinear Dirac equations with cubic terms and moving boundary. For the initial data with bounded $L^2$ norm and the suitable boundary conditions, the global existence and…

The initial-boundary value problem for the two-dimensional regular four-velocity discrete Boltzmann system is analyzed in a rectangle. The existence and uniqueness of a classical global positive solution, bounded with its first partial…

We focus on the initial boundary value problem for a general scalar balance law in one space dimension. Under rather general assumptions on the flux and source functions, we prove the well-posedness of this problem and the stability of its…

This paper concerns the initial-boundary value problem to 2D micropolar equations without angular viscosity in a smooth bounded domain. It is shown that such a system admits a unique and global weak solution. The main idea of this paper is…

We establish existence and uniqueness results for initial boundary value problems with nearly incompressible vector fields. We then apply our results to establish well-posedness of the initial-boundary value problem for the Keyfitz and…

In this paper we consider an initial boundary value problem for a semilinear parabolic equation with nonlinear nonlocal boundary condition. We prove comparison principle, the existence theorem of a local solution and study the problem of…

This paper investigates the initial boundary value problem for a fractional pseudo-parabolic equation with singular potential. The global existence and blow-up of solutions to the initial boundary value problem are obtained at low initial…