Related papers: Interacting vacuum at infinity
Earlier studies have shown that, in a two component model of the universe with dark matter and the running vacuum energy which is phenomenologically a combination of $H^2$ and $\dot{H},$ produces either eternal deceleration or acceleration…
In this letter, a coupled system of viscous Burgers' equations with zero Dirichlet boundary conditions and appropriate initial data is considered. For the well-known single viscous Burgers' equation with zero Dirichlet boundary conditions,…
Matter interacting classically with gravity in 3+1 dimensions usually gives rise to a continuum of degrees of freedom, so that, in any attempt to quantize the theory, ultraviolet divergences are nearly inevitable. Here, we investigate…
Non-autonomous differential equations exhibit a highly intricate dynamics, and various concepts have been introduced to describe their qualitative behavior. In general, it is rare to obtain time dependent invariant compact attracting sets…
We prove the existence of a compact, finite dimensional, global attractor for a coupled PDE system comprising a nonlinearly damped semilinear wave equation and a nonlinear system of thermoelastic plate equations, without any mechanical…
After a short review of the history and problems of relativistic Hamiltonian mechanics with action-at-a-distance inter-particle potentials, we study isolated two-body systems in the rest-frame instant form of dynamics. We give explicit…
We discuss the existence of pullback attractors for multivalued dynamical systems on metric spaces. Such attractors are shown to exist without any assumptions in terms of continuity of the solution maps, based only on minimality properties…
We consider an autonomous system of partial differential equations for one-dimensional distributed medium with periodic boundary conditions. Dynamics in time consists of alternating birth and death of patterns with spatial phases…
It is proven that the Wahlquist perfect fluid space-time cannot be smoothly joined to an exterior asymptotically flat vacuum region. The proof uses a power series expansion in the angular velocity, to a precision of the second order. In…
In this paper we intend to present a unified treatment of a variety of singular interacting particle systems and their McKean-Vlasov limits. This unified approach is based on the use of the relative entropy on the path space in the spirit…
A system is studied in which initially a strong classical electric field exists within an infinitely-long cylinder and no charges are present. Subsequently, within the cylinder, pairs of charged particles tunnel out from the vacuum and the…
We examine the dynamics of FLRW cosmologies in which the vacuum interacts with a perfect fluid through an energy exchange, focusing on the exploration of nonsingular configurations, including cyclic and bouncing models. We consider two…
Models of the universe with arbitrary (non gravitational) interaction between the components of the cosmic fluid: the phantom energy and the background, are investigated. A general form of the interaction that is inspired in scalar-tensor…
The most general one dimensional reaction-diffusion model with nearest-neighbor interactions solvable through the empty interval method, and without any restriction on the particle-generation from two adjacent empty sites is studied. It is…
We consider the dynamics of finite systems of point masses which move along the real line. We suppose the particles interact pairwise and undergo perfectly inelastic collisions when they collide. In particular, once particles collide, they…
We find exact solutions leading to power law accelerated expansion for a homogeneous, isotropic and spatially flat universe, dominated by an interacting mixture of cold dark matter and a tachyonic field such that the ratio of the energy…
Relativistic action-at-a-distance theories with interactions that propagate at the speed of light in vacuum are investigated. We consider the most general action depending on the velocities and relative positions of the particles. The…
We study the global dynamics of the universe within the framework of the Interacting Dark Matter (IDM) scenario. Assuming that the dark matter obeys the collisional Boltzmann equation, we can derive analytical solutions of the global…
We examine the dynamical implications of an interaction between some of the fluid components of the universe. We consider the combination of three matter components, one of which is a perfect fluid and the other two are interacting. The…
Using dynamical systems theory and a detailed numerical analysis, the late-time behaviour of tilting perfect fluid Bianchi models of types IV and VII$_h$ are investigated. In particular, vacuum plane-wave spacetimes are studied and the…