Related papers: Generalised hyperbolicity: hypersurface singularit…
Global monochromatic solutions of the scalar wave equation are obtained in flat wormholes of dimensions 2+1 and 3+1. The solutions are in the form of infinite series involving cylindirical and spherical wave functions and they are…
We study one-dimensional linear hyperbolic systems with $L^{\infty}$-coefficients subjected to periodic conditions in time and reflection boundary conditions in space. We derive a priori estimates and give an operator representation of…
In this paper, we consider the initial value problem for the Einstein-Vlasov-Scalar field equations in temporal gauge, where the initial data are prescribed on two characteristic smooth intersecting hypersurfaces. From a suitable choice of…
We investigate the existence and the global causal structure of plane symmetric spacetimes with weak regularity when the matter consists of an irrotational perfect fluid with pressure equal to its mass-energy density. Our theory encompasses…
A weak formulation for the so-called "semilinear strongly damped wave equation with constraint" is introduced and a corresponding notion of solution is defined. The main idea in this approach consists in the use of duality techniques in…
Global hyperbolicity is a central concept in Mathematical Relativity. Here, we review the different approaches to this concept explaining both, classical approaches and recent results. The former includes Cauchy hypersurfaces, naked…
An important question in mathematical relativity theory is that of the nature of spacetime singularities. The equations of general relativity, the Einstein equations, are essentially hyperbolic in nature and the study of spacetime…
A new solvable hyperbolic single wave potential is found by expanding the regular solution of the 1D Schr\"odinger equation in terms of square integrable basis. The main characteristic of the basis is in supporting an infinite tridiagonal…
There is a few results about the global stability of nontrivial solutions to quasilinear wave equations. In this paper we are concerned with the uniqueness and stability of traveling waves to the time-like extremal hypersurface in Minkowski…
This paper investigates the initial boundary value problem for a fractional pseudo-parabolic equation with singular potential. The global existence and blow-up of solutions to the initial boundary value problem are obtained at low initial…
Two geometrical well-posed hyperbolic formulations of general relativity are described. One admits any time-slicing which preserves a generalized harmonic condition. The other admits arbitrary time-slicings. Both systems have only the…
In certain models of conformal gravity, the propagation of gravitational waves is governed by a fourth order scalar partial differential equation. We study the initial value problem for a generalization of this equation, and derive a…
We prove the global classical solvability of initial-boundary problems for semilinear first-order hyperbolic systems subjected to local and nonlocal nonlinear boundary conditions. We also establish lower bounds for the order of nonlinearity…
We classify all real hypersurfaces with three distinct constant principal curvatures in complex hyperbolic spaces of dimension greater than two.
It is sometimes claimed that Lorentz invariant wave equations which allow superluminal propagation exhibit worse predictability than subluminal equations. To investigate this, we study the Born-Infeld scalar in two spacetime dimensions.…
In this paper we prove that the cubic wave equation is globally well - posed and scattering for radial initial data lying in a slightly supercritical Sobolev space, and a weighted Sobolev space.
Formulas are derived for solutions of many-body wave scattering problems by small particles in the case of acoustically soft, hard, and impedance particles embedded in an inhomogeneous medium. The limiting case is considered, when the size…
We prove some sharp regularity results for solutions of classical first order hyperbolic initial boundary value problems. Our two main improvements on the existing litterature are weaker regularity assumptions for the boundary data and…
We introduce a class of space-times modeling singular events such as evaporating black holes and topology changes, which we dub as semi-globally hyperbolic space-times. On these space-times we aim to study the existence of reasonable…
We discuss several topics related to the notion of strong hyperbolicity which are of interest in general relativity. After introducing the concept and showing its relevance we provide some covariant definitions of strong hyperbolicity. We…