相关论文: Generalized Euclidean stars with equation of state

We consider the reaction-diffusion problem $-\Delta_g u = f(u)$ in $\mathcal{B}_R$ with zero Dirichlet boundary condition, posed in a geodesic ball $\mathcal{B}_R$ with radius $R$ of a Riemannian model $(M,g)$. This class of Riemannian…

We study shear-free spherically symmetric relativistic gravitating fluids with heat flow and electric charge. The solution to the Einstein-Maxwell system is governed by the generalised pressure isotropy condition which contains a…

We present a class of exact solutions of Einstein's gravitational field equations describing spherically symmetric and static anisotropic stellar type configurations. The solutions are obtained by assuming a particular form of the…

We study the dynamics of a degenerate parabolic equation with a variable, generally non-smooth diffusion coefficient, which may vanish at some points or be unbounded. We show the existence of a global branch of nonnegative stationary…

In this paper, we continue our study [16] on the long time dynamics of radial solutions to defocusing energy critical wave equation with a trapping radial potential in 3 + 1 dimensions. For generic radial potentials (in the topological…

We seek exact solutions to the Einstein field equations which arise when two spacetime geometries are conformally related. Whilst this is a simple method to generate new solutions to the field equations, very few such examples have been…

The study of the relation between Lie algebras and groups, and especially the derivation of new algebras from them, is a problem of great interest in mathematics and physics, because finding a new Lie group from an already known one also…

This paper presents the class of solutions to the Einstein field equations for the uncharged static spherically symmetric compact object PSR J0952-0607 by using Generalized Tolman-Kuchowicz space-time metric with quadratic equation of…

We study equilibrium states in relativistic galactic dynamics which are described by solutions of the Einstein-Vlasov system for collisionless matter. We recast the equations into a regular three-dimensional system of autonomous first order…

An integrable hierarchies connected with linear stationary Schr\"odinger equation with energy dependent potentials (in general case) are considered. Galilei-like and scaling invariance transformations are constructed. A symmetry method is…

The general relativity is the base for any exact evolutionary theory of large scale structures. We calculate the universal 2+1-dimensional plane equations of gravitational field in general relativity. Based on the equations, the evolutions…

Quantum master equations are an important tool in quantum optics and quantum information theory. For systems comprising a small to medium number of atoms (or qubits), the non-truncated equations are usually solved numerically. In this…

We discuss various compatibility criteria for overdetermined systems of PDEs generalizing the approach to formal integrability via brackets of differential operators. Then we give sufficient conditions that guarantee that a PDE possessing a…

In a series of articles we describe a novel class of geometrical models of relativistic stars. Our approach to the static spherically symmetric solutions of Einstein equations is based on a careful physical analysis of radial gauge…

We construct a graded Lie algebra in which a solution to the vacuum Einstein equations is any element of degree 1 whose bracket with itself is zero. Each solution generates a cochain complex, whose first cohomology is linearized gravity…

A general reaction-diffusion equation with spatiotemporal delay and homogeneous Dirichlet boundary condition is considered. The existence and stability of positive steady state solutions are proved via studying an equivalent…

We introduce a new method for numerically evolving the full Einstein field equations in situations where the spacetime is dominated by a known background solution. The technique leverages the knowledge of the background solution to subtract…

We study radial perturbations of general relativistic stars with elastic matter sources. We find that these perturbations are governed by a second order differential equation which, along with the boundary conditions, defines a…

In this article, the ray tracing method is studied beyond the classical geometrical theory. The trajectories are here regarded as geodesics in a Riemannian manifold, whose metric and topological properties are those induced by the…

In this paper we introduce the notion of generalized Lie algebroid and we develop a new formalism necessary to obtain a new solution for the Weistein's Problem. Many applications emphasize the importance and the utility of this new…