Related papers: Characteristic initial value problems for the Eins…

Axially symmetric, stationary solutions of the Einstein-Maxwell equations with disconnected event horizon are studied by developing a method of explicit integration of the corresponding boundary-value problem. This problem is reduced to…

In this study, we consider the numerical solution of the Neumann initial boundary value problem for the wave equation in 2D domains. Employing the Laguerre transform with respect to the temporal variable, we effectively transform this…

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…

In this paper, we are concerned with the initial-boundary value problem to the 2D magneto-micropolar system with zero angular viscosity in a smooth bounded domain. We prove that there exists a unique global strong solution of such a system…

We consider the Cauchy problem for the (non-linear) Maxwell-Charged-Scalar-Field equations with spherically symmetric initial data, on a sub-extremal Reissner--Nordstr\"{o}m or Schwarzschild exterior space-time. We prove that the solutions…

In this paper we consider the initial-boundary value problem for the time-dependent Maxwell-Schr\"{o}dinger equations, which arises in the interaction between the matter and the electromagnetic field for the semiconductor quantum devices. A…

We prove local well-posedness for the initial-boundary-value problem associated to some quadratic nonlinear Schr\"odinger equations on the half-line. The results are obtained in the low regularity setting by introducing an analytic family…

An initial-boundary value problem for a time-fractional subdiffusion equation with an arbitrary order elliptic differential operator is considered. Uniqueness and existence of the classical solution of the posed problem are proved by the…

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…

A strongly well-posed initial boundary value problem based upon constraint-preserving boundary conditions of the Sommerfeld type has been established for the harmonic formulation of the vacuum Einstein's equations. These Sommerfeld…

In the 3+1 framework of the Einstein equations for the case of vanishing shift vector and arbitrary lapse, we calculate explicitly the four boundary equations arising from the vanishing of the projection of the Einstein tensor along the…

We investigate an initial-boundary value problem for a quasilinear nonhomogeneous, anisotropic Maxwell system subject to an absorbing boundary condition of Silver & M\"uller type in a smooth, bounded, strictly star-shaped domain of…

The coupled system of the spherically symmetric Einstein--Maxwell differential equations is solved under two different source conditions: non-zero electric charge and pressure anisotropy. Expressions for the metric functions, and pressures…

New exact solution of the cylindrically symmetric Einstein-Maxwell equations is presented. The solution is singular on the axis of symmetry and at the radial infinity, where sources should be placed. The accepted source at the origin can be…

We study the local and global wellposedness of the initial-boundary value problem for the biharmonic Schr\"odinger equation on the half-line with inhomogeneous Dirichlet-Neumann boundary data. First, we obtain a representation formula for…

We consider a gravitating system consisting of a scalar field minimally coupled to gravity with a self-interacting potential and an U(1) electromagnetic field. Solving the coupled Einstein-Maxwell-scalar system we find exact hairy charged…

Maximally dissipative boundary conditions are applied to the initial-boundary value problem for Einstein's equations in harmonic coordinates to show that it is well-posed for homogeneous boundary data and for boundary data that is small in…

We study the equations of motion for a barotropic fluid in spherical symmetric flow. Making use of the Riemann invariants we consider the characteristic form of these equations. In a first part, we show that the resulting constraint…

We discuss a gauge fixing of gravity coupled to a scalar field in spherical symmetry such that the Hamiltonian is an integral over space of a local density. In a previous paper we had presented it using Ashtekar's new variables. Here we…

We analyze Einstein's vacuum field equations in generalized harmonic coordinates on a compact spatial domain with boundaries. We specify a class of boundary conditions which is constraint-preserving and sufficiently general to include…