Related papers: The characteristic initial value problem for the c…
We study the plane-symmetric collision of two gravitational waves and describe the global spacetime geometry generated by this collision. To this end, we formulate the characteristic initial value problem for the Einstein equations, when…
For a massive scalar field in a fixed Schwarzschild background, the radial wave equation obeyed by Fourier modes is first studied. After reducing such a radial wave equation to its normal form, we first study approximate solutions in the…
We consider a unique continuation problem for the wave equation given data in a volumetric subset of the space time domain. In the absence of data on the lateral boundary of the space-time cylinder we prove that the solution can be…
The null-timelike initial-boundary value problem for a hyperbolic system of equations consists of the evolution of data given on an initial characteristic surface and on a timelike worldtube to produce a solution in the exterior of the…
It is an open question whether solutions of the Einstein-Euler equations are smooth enough to admit locally inertial coordinates at points of shock wave interaction, or whether "regularity singularities" can exist at such points. The term…
We consider self-gravitating fluids in cosmological spacetimes with Gowdy symmetry on the torus $T^3$ and, in this class, we solve the singular initial value problem for the Einstein-Euler system of general relativity, when an initial data…
In this work a new numerical technique to prepare Cauchy data for the initial value problem (IVP) formulation of Einstein's field equations is presented. Directly inspired by the exterior asymptotic gluing (EAG) result of Corvino (2000) our…
The spatially periodic initial problem and Cauchy problem for nonlinear Schr\"odinger equations are considered. The existence and uniqueness of global solution with infinite smooth initial data $u_0$, i.e. $u_0,\;|u_0|^{2p}u_0\in…
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…
We consider the initial boundary value problem of non-homogeneous stochastic heat equation. The derivative of the solution with respect to time receives heavy random perturbation. The space boundary is Lipschitz and we impose non-zero…
We analyze existence and properties of solutions of two-dimensional general relativistic initial data sets with a negative cosmological constant, both on spacelike and characteristic surfaces. A new family of such vacuum, spacelike data…
We take a step towards characterising stationary data for the vacuum Einstein equations, by finding a necessary condition on initial data for which the evolution is a solution of the vacuum equations admitting a Killing vector, which is…
We consider the defocusing nonlinear wave equation of power-type on $\mathbb{R}^3$. We establish an almost sure global existence result with respect to a suitable randomization of the initial data. In particular, this provides examples of…
We consider the scalar wave equation $\square_g \phi$ and the linearized Einstein-scalar field system around generalized Kasner spacetimes with spatial topology $\mathbb{T}^D$. In suitable regimes for the Kasner exponents, it is known that…
As is known, the problems for the differential equations with continuously changing order of the derivatives are not considered completely. In this paper we consider the initial and boundary value problems for this type of linear ordinary…
We review various aspects of the characteristic initial value problem for the Einstein equations, presenting new approaches to some of the issues arising.
We study deformations of axially symmetric initial data for Einstein-Maxwell equations satisfying the time-rotation ($t$-$\phi$) symmetry and containing one asymptotically cylindrical end and one asymptotically flat end. We find that the…
We consider equations of M\"uller-Israel-Stewart type describing a relativistic viscous fluid with bulk viscosity in four-dimensional Minkowski space. We show that there exists a class of smooth initial data that are localized perturbations…
Generalizing earlier results on the initial data and the final fate of dust collapse, we study here the relevance of the initial state of a spherically symmetric matter cloud towards determining its end state in the course of a continuing…
We consider the Einstein-Maxwell-fluid constraint equations, and make use of the conformal method to construct and parametrize constant-mean-curvature hyperboloidal initial data sets that satisfy the shear-free condition. This condition is…