相关论文: Hyperbolicity of Hamiltonian formulations in Gener…

In this small paper, we study a boundary value problem for an equation of parabolic-hyperbolic type. The goal is to show how we can prove existence and uniqueness theorem for a regular solution.

The purpose of this article is to demonstrate that i) the framework of elliptic hypergeometric integrals (EHIs) can be extended by input from supersymmetric gauge theory, and ii) analyzing the hyperbolic limit of the EHIs in the extended…

We discuss several classes of linear second order initial-boundary value problems, where damping terms appear in the main wave equation as well as in the dynamic boundary condition. We investigate their well-posedness and describe some…

Based on empirical evidence, quantum systems appear to be strictly linear and gauge invariant. This work uses concise mathematics to show that quantum eigenvalue equations on a one dimensional ring can either be gauge invariant or have a…

It was shown recently that the constraints on the initial data for Einstein's equations may be posed as an evolutionary problem [9]. In one of the proposed two methods the constraints can be replaced by a first order symmetrizable…

We study a Neumann type initial-boundary value problem for strongly degenerate parabolic-hyperbolic equations under the nonlinearity-diffusivity condition. We suggest a notion of entropy solution for this problem and prove its uniqueness.…

We show, for some classes of diffusion coefficients that, generically in f, all equilibria of the reaction-diffusion equation u_t = (a(x)u_x)_x + f(u) with homogeneous Neumann boundary conditions are hyperbolic.

A common approach for the numerical simulation of wave propagation on a spatially unbounded domain is to truncate the domain via an artificial boundary, thus forming a finite computational domain with an outer boundary. Absorbing boundary…

Considered herein is the initial-value problem for the generalized periodic Camassa-Holm equation which is related to the Camassa-Holm equation and the Hunter-Saxton equation. Sufficient conditions guaranteeing the development of breaking…

For various theories, in particular gauge field theories, the algebraic form of the Hamiltonian simplifies considerably if one writes it in terms of certain complex variables. Also general relativity when written in the new canonical…

Recently, Haase and Ilten initiated the study of classifying algebraically hyperbolic surfaces in toric threefolds. We complete this classification for $\mathbb{P}^1 \times \mathbb{P}^1 \times \mathbb{P}^1$, $\mathbb{P}^2 \times…

We show that Einstein equations are compatible with the presence of massive point particle idealization and find the corresponding two parameter family of solutions. They are complete defined by the bare mechanical mass $M>0$ and the…

Cauchy initial value problem on a hyperboloid is proved to define a Hamiltonian system, provided the radiation data at null infinity are also taken into account, as a part of Cauchy data. The "Trautman-Bondi mass", supplemented by the…

It is described how the standard Poisson bracket formulas should be modified in order to incorporate integrals of divergences into the Hamiltonian formalism and why this is necessary. Examples from Einstein gravity and Yang-Mills gauge…

We find new classes of exact solutions of the initial momentum constraint for vacuum Einstein's equations. Considered data are either invariant under a continuous symmetry or they are assumed to have the exterior curvature tensor of a…

Second-order formulations of the 3+1 Einstein equations obtained by eliminating the extrinsic curvature in terms of the time derivative of the metric are examined with the aim of establishing whether they are well posed, in cases of…

Symmetric hyperbolic systems of equations are explicitly constructed for a general class of tensor fields by considering their structure as r-fold forms. The hyperbolizations depend on 2r-1 arbitrary timelike vectors. The importance of the…

We consider $n+1$ dimensional smooth Riemannian and Lorentzian spaces satisfying Einstein's equations. The base manifold is assumed to be smoothly foliated by a one-parameter family of hypersurfaces. In both cases---likewise it is usually…

We explore the new physics phenomena of gravidynamics governed by the inhomogeneous spin gauge symmetry based on the gravitational quantum field theory. Such a gravidynamics enables us to derive the generalized Einstein equation and an…

We discuss the initial-boundary value problem of General Relativity. Previous considerations for a toy model problem in electrodynamics motivate the introduction of a variational principle for the lapse with several attractive properties.…