Related papers: The initial-boundary value problem for the Kawahar…
This paper is concerned with the study of the well-posedeness for the initial boundary value problem to the time-fractional wave equation with acoustic boundary conditions. The problem is considered in a bounded and connected domain $\Omega…
We study a mixed initial-boundary value problem for the Navier-Stokes equations, where the Dirichlet, Neumann and slip boundary conditions are prescribed on the faces of a three-dimensional polyhedral domain. We prove the existence,…
The paper develops a theory of spectral boundary value problems from the perspective of general theory of linear operators in Hilbert spaces. An abstract form of spectral boundary value problem with generalized boundary conditions is…
We propose a fast algorithm for the probabilistic solution of boundary value problems (BVPs), which are ordinary differential equations subject to boundary conditions. In contrast to previous work, we introduce a Gauss--Markov prior and…
The aim of the paper is to develop a general theory of solvability of linear inhomogeneous boundary-value problems for systems of ordinary differential equations of arbitrary order in Sobolev spaces. Boundary conditions are allowed to be…
In this work we present Haar wavelet collocation method and solve the following class of system of Lane-Emden equation defined as \begin{eqnarray*} -(t^{k_1} y'(t))'=t^{-\omega_1} f_1(t,y(t),z(t)),\\ -(t^{k_2} z'(t))'=t^{-\omega_2}…
In this paper we study the initial boundary value problem for the system\\ $-\mbox{{div}}\left[(I+\mathbf{m} \mathbf{m}^T)\nabla p\right]=s(x),\ \…
The initial value problem (IVP) for the non-isotropic Schr\"odinger equation posed on the two-dimensional cylinders and $\mathbb{T}^2$ is considered. The IVP is shown to be locally well-posed for small initial data in…
We discuss initial-boundary value problems of arbitrary spatial order subject to arbitrary boundary conditions. We formalise the concept of the conditioning of such a problem and show that it represents a necessary criterion for…
Recently, the eigenvalue problems formulated with symmetric positive definite bilinear forms have been well investigated with the aim of explicit bounds for the eigenvalues. In this paper, the existing theorems for bounding eigenvalues are…
The paper is concerned with the following $n\times n$ Dirac type equation$$Ly=-iB(x)^{-1}(y'+Q(x)y)=\lambda y, \quad B(x)=B(x)^*,\quad y={\rm col}(y_1,\ldots,y_n),\quad x\in[0,\ell],$$ on a finite interval $[0,\ell]$. Here $Q$ is a summable…
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 considers to the problems of diffraction of electromagnetic waves on a half-plane, which has a finite inclusion in the form of a Lipschitz curve. The diffraction problem formulated as boundary value problem for Helmholtz…
This paper is concerned with the initial-boundary value problem for the Einstein equations in a first-order generalized harmonic formulation. We impose boundary conditions that preserve the constraints and control the incoming gravitational…
We consider operator-valued boundary value problems in $(0,2\pi)^n$ with periodic or, more generally, $\nu$-periodic boundary conditions. Using the concept of discrete vector-valued Fourier multipliers, we give equivalent conditions for the…
In this note we devise and analyse well-posed variational formulations and operator theoretical methods for boundary value problems associated to the biharmonic operator. Of particular interest are Neumann type and over- and underdetermined…
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…
We investigate an initial-boundary value problem for a time-fractional subdiffusion equation with the Caputo derivatives on $N$-dimensional torus by the classical Fourier method. Since our solution is established on the eigenfunction…
We consider the initial value problem associated to the inhomogeneous nonlinear Schr\"o\-din\-ger equation, \begin{equation} iu_t + \Delta u +\mu|x|^{-b}|u|^{\alpha}u=0, \quad u_0\in H^s(\mathbb R^N) \text{ or } u_0 \in\dot H ^s(\mathbb…
We develop a well-posedness theory for second order systems in bounded domains where boundary phenomena like glancing and surface waves play an important role. Attempts have previously been made to write a second order system consisting of…