Related papers: Initial boundary value problems for Einstein's fie…
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…
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…
In this paper, we consider an initial boundary value problem for Maxwell's equations. For this hyperbolic type problem, we derive guaranteed and computable upper bounds for the difference between the exact solution and any pair of vector…
This article deals with the initial-boundary value problem for a moderately coupled system of time-fractional diffusion equations. Defining the mild solution, we establish fundamental unique existence, limited smoothing property and…
In this paper, complex Ginzburg-Landau (CGL) equations governed by p-Laplacian are studied. We discuss the global existence of solutions for the initial-boundary value problem of the equation in general domains. The global solvability of…
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…
This paper is concerned with the initial-boundary value problem \; for stochastic transport equations in bounded domains. For a given stochastic perturbation of the drift vector field, we prove existence and uniqueness of weak solutions…
We present a set of well-posed constraint-preserving boundary conditions for a first-order in time, second-order in space, harmonic formulation of the Einstein equations. The boundary conditions are tested using robust stability, linear and…
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…
We consider the spectral structure of indefinite second order boundary-value problems on graphs. A variational formulation for such boundary-value problems on graphs is given and we obtain both full and half-range completeness results. This…
Outer boundary conditions for strongly and symmetric hyperbolic formulations of 3D Einstein's field equations with a live gauge condition are discussed. The boundary conditions have the property that they ensure constraint propagation and…
We consider an initial mixed-boundary value problem for anisotropic fractional type degenerate parabolic equations posed in bounded domains. Namely, we consider that the boundary of the domain splits into two parts. In one of them, we…
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…
We discuss the initial-boundary value problem for the Baumgarte-Shapiro-Shibata-Nakamura evolution system of Einstein's field equations which has been used extensively in numerical simulations of binary black holes and neutron stars. We…
We prove existence, uniqueness and regularity results for mixed boundary value problems associated with fully nonlinear, possibly singular or degenerate elliptic equations. Our main result is a global H\"older estimate for solutions,…
We consider the initial boundary value problem for a model system of one-dimensional equations which describe unsteady polytropic motions of a mixture of viscous compressible fluids. We prove the global existence and uniqueness theorem for…
We analyse the issue of uniqueness of solutions of the static vacuum Einstein equations with prescribed geometric or Bartnik boundary data. Large classes of examples are constructed where uniqueness fails. We then discuss the implications…
We consider initial boundary value problems with the homogeneous Neumann boundary condition. Given an initial value, we establish the uniqueness in determining a spatially varying coefficient of zeroth-order term by a single measurement of…
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.
We propose a geometric approach for the numerical integration of singular initial value problems for (systems of) quasi-linear differential equations. It transforms the original problem into the problem of computing the unstable manifold at…