相关论文: Initial Value Problems and Signature Change

We analyze the initial value problem for scalar fields obeying the Klein-Gordon equation. The standard Cauchy initial value problem for second order differential equation is to construct a solution function in a neighborhood of space and…

Motivated by the initial value problem in semiclassical gravity, we study the initial value problem of a system consisting of a quantum scalar field weakly interacting with a classical one. The quantum field obeys a Klein-Gordon equation…

We study the semiclassical Einstein field equations with a Klein-Gordon field in ultrastatic and static spacetimes. In both cases, the equations for the spacetime metric become constraint equations. In the ultrastatic case, the Hadamard…

While there exist now formulations of initial boundary value problems for Einstein's field equations which are well posed and preserve constraints and gauge conditions, the question of geometric uniqueness remains unresolved. For two…

We provide a formulation of the initial boundary value problem for Friedrich's extended conformal Einstein field equations in which boundary data is prescribed on a timelike hypersurface located at a finite position in the spacetime. Our…

Kossowski and Kriele derived boundary conditions on the metric at a surface of signature change. We point out that their derivation is based not only on certain smoothness assumptions but also on a postulated form of the Einstein field…

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 consider the (massless) scalar field on a 2-dimensional manifold with metric that changes signature from Lorentzian to Euclidean. Requiring a conserved momentum in the spatially homogeneous case leads to a particular choice of…

We consider perturbations of the semiclassical Schr{\"o}dinger equation on a compact Riemannian surface with constant negative curvature and without boundary. We show that, for scales of times which are logarithmic in the size of the…

We initiate the study of the spherically symmetric Einstein-Klein-Gordon system in the presence of a negative cosmological constant, a model appearing frequently in the context of high-energy physics. Due to the lack of global hyperbolicity…

A signature changing spacetime is one where an initially Riemannian manifold with Euclidean signature evolves into the Lorentzian universe we see today. This concept is motivated by problems in causality implied by the isotropy and…

We study the solutions to the Klein-Gordon equation for the massive scalar field in the universal covering space of two-dimensional anti-de Sitter space. For certain values of the mass parameter, we impose a suitable set of boundary…

We prove, by adapting the method of Colliander-Kenig (2002), local well-posedness of the initial-boundary value problem for the one-dimensional nonlinear Schroedinger equation on the half-line under low boundary regularity assumptions.

In this article we will study the initial value problem for some Schr\"odinger equations with Diraclike initial data and therefore with infinite L2 mass, obtaining positive results for subcritical nonlinearities. In the critical case and in…

We consider a characteristic initial value problem for a class of symmetric hyperbolic systems with initial data given on two smooth null intersecting characteristic surfaces. We prove existence of solutions on a future neighborhood of 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…

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…

There exists a widespread belief that signature type change could be used to avoid spacetime singularities. We show that signature change cannot be utilised to this end unless the Einstein equation is abandoned at the suface of signature…

We consider the one-dimensional linear free space Schr\"odinger equation on a bounded interval subject to homogeneous linear boundary conditions. We prove that, in the case of pseudoperiodic boundary conditions, the solution of the…

Initial-boundary value problems in a bounded rectangle with different types of boundary conditions for two-dimensional Zakharov-Kuznetsov equation are considered. Results on global well-posedness in the classes of weak and regular solution…