Related papers: Analysis of a Bianchi-like equation satisfied by t…
Lorentzian manifolds with parallel spinors are important objects of study in several branches of geometry, analysis and mathematical physics. Their Cauchy problem has recently been discussed by Baum, Leistner and Lischewski, who proved that…
We investigate the global solutions of the Dirac equation on the Anti-de-Sitter Universe. Since this space is not globally hyperbolic, the Cauchy problem is not, {\it a priori}, well-posed. Nevertheless we can prove that there exists…
We look for sufficient conditions such that the scalar curvature, Ricci and Kretchmann scalars be bounded in Hyperextended Scalar Tensor theory for Bianchi models. We find classes of gravitation functions and Brans-Dicke coupling functions…
In this paper, we deal with Serrin-type problems in Riemannian manifolds. First, we obtain a Heintze-Karcher inequality and a Soap Bubble result, with its respective rigidity, when the ambient space has a Ricci tensor bounded below. After,…
Multidimensional Consistency becomes more and more important in the theory of discrete integrable systems. Recently, we gave a classification of all 3D consistent 6-tuples of equations with the tetrahedron property, where several novel…
In this paper, we investigate Bianchi type-$VI$ cosmological model for the universe filled with dark energy and viscous fluid in the presence of cosmological constant. Also, we show accelerating expansion of the universe by drawing volume…
Recently, the authors proved [2] that the Maxwell-Stefan system with an incompressibility-like condition on the total flux can be rigorously derived from the multi-species Boltzmann equation. Similar cross-diffusion models have been widely…
Let $X$ be a smooth $n\,$-dimensional manifold and $D$ be an open connected set in $X$ with smooth boundary $\partial D$. Perturbing the Cauchy problem for an elliptic system $Au = f$ in $D$ with data on a closed set $\iG \subset \partial…
On the one hand, we investigate the existence and pathwise uniqueness of a nonnegative martingale solution to the stochastic evolution system of nonlinear advection-diffusion equations proposed by Klausmeier with Gaussian multiplicative…
This paper studies a space-inhomogeneous Boltzmann-Nordheim equation with pseudo-Maxwellian forces. Strong solutions are obtained for the Cauchy problem in a setting with large bounded L1 initial data. The main results are existence,…
The stability of isotropic cosmological solutions in the Bianchi I model is considered. We prove that the stability of isotropic solutions in the Bianchi I metric for a positive Hubble parameter follows from their stability in the…
The computational analysis of the Cauchy problem for semi-linear Klein-Gordon equations in the de Sitter spacetime is considered. Several simulations are performed to show the time-global behaviors of the solutions of the equations in the…
Spatially homogeneous but totally anisotropic and non-flat Bianchi type II cosmological model has been studied in general relativity in the presence of two minimally interacting fluids; a perfect fluid as the matter fluid and a hypothetical…
The present work discusses about the existence of compact star model in the context of $f(R,T)$ gravity with $R$ as the Ricci scalar and $T$ as the trace of energy-momentum tensor $T_{\mu \nu}$. The model has been developed by considering…
A Bianchi type-I cosmological model in the presence of a magnetic flux along a cosmic string is investigated. A nonlinear spinor field is used to simulate the cosmological cloud of strings. It is shown that the spinor field simulation offer…
We show how the Apparently Noninvariant Terms (ANTs), which emerge in perturbation theory of nonlinear sigma models, are consistent with the nonlinearly realized symmetry by employing the Ward-Takahashi identity (in the form of an…
The standard cosmological model is challenged by an ever-growing collection of observations, which invites (and stimulates) inquiry into possible additions and/or alterations. One such alteration comes from letting cosmic isotropy -- as…
In the present manuscript we consider the Boltzmann equation that models a polyatomic gas by introducing one additional continuous variable, referred to as microscopic internal energy. We establish existence and uniqueness theory in the…
We construct polynomial conformal invariants, the vanishing of which is necessary and sufficient for an $n$-dimensional suitably generic (pseudo-)Riemannian manifold to be conformal to an Einstein manifold. We also construct invariants…
We study a convergence criterion which generalises the notion of being monotonically decreasing, and introduce a quantitative version of this criterion, a so called metastable rate of asymptotic decreasingness. We then present a concrete…