Related papers: A model problem for the initial-boundary value for…
A formulation of Einstein equations is presented that could yield advantages in the study of collisions of binary compact objects during regimes between linear-nonlinear transitions. The key idea behind this formulation is a separation of…
In this paper, we deal with analysis of the initial-boundary value problems for the semilinear time-fractional diffusion equations, while the case of the linear equations was considered in the first part of the present work. These equations…
The main objective of this paper is analysis of the initial-boundary value problems for the linear time-fractional diffusion equations with a uniformly elliptic spatial differential operator of the second order and the Caputo type…
We derive an initial value formulation for dynamical Chern-Simons gravity, a modification of general relativity involving parity-violating higher derivative terms. We investigate the structure of the resulting system of partial differential…
We use the conformal method to obtain solutions of the Einstein-scalar field gravitational constraint equations. Handling scalar fields is a bit more challenging than handling matter fields such as fluids, Maxwell fields or Yang-Mills…
In recent time, by working in a plane with the metric associated with wave equation (the Special Relativity non-definite quadratic form), a complete formalization of space-time trigonometry and a Cauchy-like integral formula have been…
We propose a novel approach to the problem of constraining cosmological initial conditions. Within the framework of effective field theory, we classify initial conditions in terms of boundary terms added to the effective action describing…
Two problems concerning asymptotically hyperbolic manifolds with an inner boundary are studied. First, we study scalar curvature presciption with either Dirichlet or mean curvature prescription interior boundary condition. Then we apply…
We discuss the problem of prescribing the mean curvature and conformal class as boundary data for Einstein metrics on 3-manifolds, in the context of natural elliptic boundary value problems for Riemannian metrics.
In this paper, new boundary differential equations for the two-dimensional exterior scattering problem have been derived. It has been shown that the Helmholtz equation can be reduced to an inhomogeneous Bessel's equation in a body-fitted…
The main result of this paper is the proof that there are local electric and magnetic field configurations expressed in terms of field lines on an arbitrary hyperbolic manifold. This electromagnetic field is described by (dual) solutions of…
We consider the Cauchy problem for the isentropic compressible Euler-Maxwell equations under general pressure laws in a three-dimensional periodic domain. For any smooth initial electron density away from the vacuum and smooth…
We provide new exact solutions to the Einstein-Maxwell system of equations which are physically reasonable. The spacetime is static and spherically symmetric with a charged matter distribution. We utilise an equation of state which is…
In physical theories, boundary or initial conditions play the role of selecting special situations which can be described by a theory with its general laws. Cosmology has long been suspected to be different in that its fundamental theory…
We construct exact solutions to the Bianchi equations on a flat spacetime background. When the constraints are satisfied, these solutions represent in- and outgoing linearized gravitational radiation. We then consider the Bianchi equations…
In a recent work, Ringstr\"om proposed a geometric notion of initial data on big bang singularities. Moreover, he conjectured that initial data on the singularity could be used to parameterize quiescent solutions to Einstein's equations;…
We present three-dimensional simulations of Einstein equations implementing a symmetric hyperbolic system of equations with dynamical lapse. The numerical implementation makes use of techniques that guarantee linear numerical stability for…
We prove several theorems concerning the connection between the local CR embeddability of 3-dimensional CR manifolds, and the existence of algebraically special Maxwell and gravitational fields. We reduce the Einstein equations for…
The initial-boundary value problem for the inhomogeneous non-cutoff Boltzmann equation is a challenging open problem. In this paper, we study the stability and long-time dynamics of the Boltzmann equation near a global Maxwellian without…
The Weiss variation of the Einstein-Hilbert action with an appropriate boundary term has been studied for general boundary surfaces; the boundary surfaces can be spacelike, timelike, or null. To achieve this we introduce an auxiliary…