Related papers: Boundary conditions in linearized harmonic gravity
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 consider initial-boundary problems for general linear first-order strictly hyperbolic systems with local or nonlocal nonlinear boundary conditions. While boundary data are supposed to be smooth, initial conditions can contain…
In recent work, we used pseudo-differential theory to establish conditions that the initial-boundary value problem for second order systems of wave equations be strongly well-posed in a generalized sense. The applications included the…
The dynamics of gravitational waves is investigated in full 3+1 dimensional numerical relativity, emphasizing the difficulties that one might encounter in numerical evolutions, particularly those arising from non-linearities and gauge…
Numerical results, based on a lattice method for computational general relativity, will be presented for Cauchy evolution of initial data for the Brill, Teukolsky and polarised Gowdy space-times. The simple objective of this paper is to…
A systematic way of generating sets of local boundary conditions on the gauge fields in a path integral is presented. These boundary conditions are suitable for one--loop effective action calculations on manifolds with boundary and for…
Initial-boundary value problem for linearized equations of motion of viscous barotropic fluid in a bounded domain is considered. Existence, uniqueness and estimates of weak solutions to this problem are derived. Convergence of the solutions…
I describe a new algorithm for solving nonlinear wave equations. In this approach, evolution takes place on characteristic hypersurfaces. The algorithm is directly applicable to electromagnetic, Yang-Mills and gravitational fields and other…
Time-periodic weak solutions for a coupled hyperbolic-parabolic system are obtained. A linear heat and wave equation are considered on two respective $d$-dimensional spatial domains that share a common $(d-1)$-dimensional interface…
This note deals with the boundary control problem of a nonhomogeneous flexible wing evolving under unsteady aerodynamic loads. The wing is actuated at its tip by flaps and is modeled by a distributed parameter system consisting of two…
We consider gauge theories from the free evolution point of view, in which initial data satisfying constraints of a theory are given. Because the constraints are compatible with the field equations they remain so. We study a model…
For the string baryon model "triangle" the initial-boundary value problem is stated and solved in general. This problem implies defining a classical motion of the system on the base of given initial position and initial velocities of string…
The purpose of this paper is to study in detail the constraint structure of the Hamiltonian and symplectic-Lagrangian descriptions for the scalar and electromagnetic fields in the presence of spatial boundaries. We carefully discuss the…
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…
In this paper we develop a geometric theory for quasilinear parabolic problems in weighted $L_p$-spaces. We prove existence and uniqueness of solutions as well as the continuous dependence on the initial data. Moreover, we make use of a…
In the Bondi-Sachs gauge, the Einstein equations with a cosmological constant coupled to a scalar field in spherical symmetry are cast into a first order strongly hyperbolic formulation in which the lapse and shift are the fundamental…
We study hyperbolic systems of one-dimensional partial differential equations under general, possibly non-local boundary conditions. A large class of evolution equations, either on individual 1-dimensional intervals or on general networks,…
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…
We present two families of first-order in time and second-order in space formulations of the Einstein equations (variants of the Arnowitt-Deser-Misner formulation) that admit a complete set of characteristic variables and a conserved energy…
In this article, we focus on a doubly nonlinear nonlocal parabolic initial boundary value problem driven by the fractional $p$-Laplacian equipped with homogeneous Dirichlet boundary conditions on a domain in $\mathbb{R}^{d}$ and composed…