Related papers: Polytropic Dynamical Systems with Time Singularity
A new development of the ``monodromy transform'' method for analysis of hyperbolic as well as elliptic integrable reductions of Einstein equations is presented. Compatibility conditions for some alternative representations of the…
In this paper we will consider the peridynamic equation of motion which is described by a second order in time partial integro-differential equation. This equation has recently received great attention in several fields of Engineering…
We construct singular solutions of a complex elliptic equation of second order, having an isolated singularity of any order. In particular, we extend results obtained for the real partial differential equation in divergence form by…
In this paper, we develop a new method to find the exact solutions of the Einstein's field equations by using which we construct time-periodic solutions. The singularities of the time-periodic solutions are investigated and some new…
A recently introduced two-phase flow model by Chun Shen is studied in this work. The model is derived to describe the dynamics of immersed water bubbles in liquid water as carrier. Several assumptions are made to obtain a reduced form of…
We study a new class of equilibrium two-parametric distribution functions of spherical stellar systems with radially anisotropic velocity distribution of stars. The models are less singular counterparts of the so called generalized…
We present a method for solving a class of initial valued, coupled, non-linear differential equations with `moving singularities' subject to some subsidiary conditions. We show that this type of singularities can be adequately treated by…
In this paper we study a class of nonlinear anisotropic parabolic problems in bounded domains. In detail, we study the influences of the initial data and the forcing term f on the behavior of the solutions. We prove existence and uniqueness…
This paper is devoted to derive some necessary and suficient conditions for the existence of positive solutions to a singular second order system of dynamic equations with Dirichlet boundary conditions. The results are obtained by employing…
Lagrangian systems with nonholonomic constraints may be considered as singular differential equations defined by some constraints and some multipliers. The geometry, solutions, symmetries and constants of motion of such equations are…
We present an approximate model of Wheeler-Feynman electrodynamics for which uniqueness of solutions is proved. It is simple enough to be instructive but close enough to Wheeler-Feynman electrodynamics such that we can discuss its natural…
We present a stability analysis of the standard nonautonomous systems type for a recently introduced generalized Lane-Emden equation which is shown to explain the presence of some of the structures observed in the atomic spatial…
We have derived exact solutions of the isothermal Lane--Emden equation with and without rotation in a cylindrical geometry. The corresponding hydrostatic equilibria are most relevant to the dynamics of the protosolar nebula before and…
We investigate the existence of inhomogeneous Szekeres spacetimes in Einstein-\ae ther theory. We show that inhomogeneous solutions which can be seen as extension of the Szekeres solutions existing in Einstein-\ae ther gravity only for a…
We introduce a nonequilibrium off--lattice model for anisotropic phenomena in fluids. This is a Lennard--Jones generalization of the driven lattice--gas model in which the particles' spatial coordinates vary continuously. A comparison…
We introduce a new method which resolves the problem of regularity and compactness of entropy solutions for nonlinear degenerate parabolic equations under non-degeneracy conditions on the sphere. In particular, we address a problem of…
We study a system of parabolic equations consisting of a double nonlinear parabolic equations of Forchheimer type coupled with a semilinear parabolic equations. The system describes a fluid-like driven system for active-passive pedestrian…
The coupled system of the spherically symmetric Einstein--Maxwell differential equations is solved under two different source conditions: non-zero electric charge and pressure anisotropy. Expressions for the metric functions, and pressures…
A wide class of non-autonomous nonlinear parabolic partial differential equations with delay is studied. We allow in our investigations different types of delays such as constant, time-dependent, state-dependent (both discrete and…
We study different types of spacetime singularities which emerge in the context of disformal electrodynamics. The latter is characterized by transformations of the background metric which preserve regular (non-null) solutions of Maxwell…