Related papers: A fifth order differential equation for charged pe…
We focus here on a class of fourth-order parabolic equations that can be written as a system of second-order equations by introducing an auxiliary variable. We design a novel second-order fully discrete mixed finite element method to…
In Newton's and in Einstein's theory we give criteria on the equation of state of a barotropic perfect fluid which guarantee that the corresponding one-parameter family of static, spherically symmetric solutions has finite extent. These…
In this work we have discussed the implications of shear-free condition on axially symmetric anisotropic gravitating objects in $f(R,T)$ theory. Restricted axial symmetry ignoring rotation and reflection enteries is taken into account for…
Longstanding problems regarding the causality of the diffusion equation are resolved through a class of exact solutions. A universal differential solution for diffusive processes is derived that is causal and exact at any analytic point in…
Spherically symmetric expansionfree distributions are systematically studied. The whole set of field equations and junction conditions are presented for a general distribution of dissipative anisotropic fluid (principal stresses unequal),…
Using an orthonormal Lorentz frame approach to axistationary perfect fluid spacetimes, we have formulated the necessary and sufficient equations as a first order system, and investigated the integrability conditions of this set of…
We find the Lie point symmetries for non-relativistic two-dimensional charged particle motion. These symmetries comprise a quasi-invariance transformation, a time-dependent rotation, a time-dependent spatial translation and a dilation. The…
New problem is considered that is to find nonlinear differential equations with special solutions. Method is presented to construct nonlinear ordinary differential equations with exact solution. Crucial step to the method is the assumption…
In the present paper we analyze and discuss some mathematical aspects of the fluid-static configurations of a self-gravitating perfect gas enclosed in a spherical solid shell. The mathematical model we consider is based on the well-known…
In this manuscript we investigate the Benjamin-Feir (or modulation) instability for the spatial evolution of water waves from the perspective of the discrete, spatial Zakharov equation, which captures cubically nonlinear and resonant wave…
A classical topic in the mathematical theory of hydrodynamics is to study the evolution of the free surface separating air from an incompressible perfect fluid. The goal of this survey is to examine this problem for two important sets of…
Static spherically symmetric solutions to the Einstein-Euler equations with prescribed central densities are known to exist, be unique and smooth for reasonable equations of state. Some criteria are also available to decide whether…
Present paper provides a new model for perfect fluid sphere filled with charge in higher dimensional spacetime admitting conformal symmetry. We consider a linear equation of state with coefficients fixed by the matching conditions at the…
We derive a five-dimensional nonlinear first order matrix PDE which is a generalization of the completely integrable (2+1)-dimensional $N$-wave equation. Similar to the $\bar\partial$-problem, our algorithm is based on the linear integral…
An algorithm based on the choice of a single monotone function (subject to boundary conditions) is presented which generates all regular static spherically symmetric perfect fluid solutions of Einstein's equations. For physically relevant…
Stationary axisymmetric perfect fluid space-times are investigated using the curvature description of geometries. Attention is focused on space-times with a vanishing electric part of the Weyl tensor. It is shown that the only…
Lie symmetry analysis is an established method for generating symmetries of differential equations. We apply this method together the generalized fundamental theorem of double reduction. In particular, Noether symmetries and some associated…
We prove the theorem: The necessary and sufficient condition for a spherically symmetric spacetime to represent an isothermal perfect fluid (barotropic equation of state with density falling off as inverse square of the curvature radius)…
We show that shearfree perfect fluids obeying an equation of state p=(gamma -1) mu are non-rotating or non-expanding under the assumption that the spatial divergence of the magnetic part of the Weyl tensor is zero.
The geometrical theory of partial differential equations in the absolute sense, without any additional structures, is developed. In particular the symmetries need not preserve the hierarchy of independent and dependent variables. The order…