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1.
We investigate the evolution of the temperature profile of a Friedmann-like collapsing sphere undergoing dissipative gravitational collapse in the form of a radial heat flux. We further consider the behavior of the star close to quasi-static equilibrium (weak heat flux approximation) and show that relaxational effects cannot be ignored. It is explicitly shown that extended irreversible thermodynamics predict a higher temperature at all interior points of the stellar configuration compared to the Eckart theory. These results carry over to the weak heat flux approximation with the magnitude of the temperature being lower than the full radiating model. The stability of the model after its departure from equilibrium is studied by considering the behavior of the control parameter throughout the stellar interior. 相似文献
2.
Dipak Kesh Debasis Mukherjee A. K. Sarkar A. B. Roy 《Journal of Applied Mathematics and Computing》1998,5(2):295-305
In this study, we have considered a prey-predator model reflecting the predator interference with discrete time delay. This delay is regarded as the lag due to gestation. In absence of delay, the criteria for existence of interior equilibrium and its global stability are derived. By choosing the delay as a bifurcation parameter, we have shown that a Hopf bifurcation may occur when the delay passes its critical value. Finally, we have derived the criteria for stability switches and verified the results through computer simulation. 相似文献
3.
Keshlan S. Govinder Barbara Abraham-Shrauner 《Nonlinear Analysis: Real World Applications》2009,10(6):3381-DECMA
Hidden symmetries of differential equations are point symmetries that arise unexpectedly in the increase (equivalently decrease) of order, in the case of ordinary differential equations, and variables, in the case of partial differential equations. The origins of Type II hidden symmetries (obtained via reduction) for ordinary differential equations are understood to be either contact or nonlocal symmetries of the original equation while the origin for Type I hidden symmetries (obtained via increase of order) is understood to be nonlocal symmetries of the original equation. Thus far, it has been shown that the origin of hidden symmetries for partial differential equations is point symmetries of another partial differential equation of the same order as the original equation. Here we show that hidden symmetries can arise from contact and nonlocal/potential symmetries of the original equation, similar to the situation for ordinary differential equations. 相似文献
4.
New theorems about the existence of solution for a system of infinite linear equations with a Vandermonde type matrix of coefficients are proved. Some examples and applications of these results are shown. In particular, a kind of these systems is solved and applied in the field of the General Relativity Theory of Gravitation. The solution of the system is used to construct a relevant physical representation of certain static and axisymmetric solution of the Einstein vacuum equations. In addition, a newtonian representation of these relativistic solutions is recovered. It is shown as well that there exists a relation between this application and the classical Haussdorff moment problem. 相似文献
5.
In this paper, we show that self-similarity with respect to the existence of a (purely radial) homothetic Killing vector field for spherically symmetric spacetimes implies the separability of the spacetime metric in terms of the co-moving coordinates (and vice versa) and that the metric is, uniquely, the one recently reported in (Class. Quantam Grav. 18: 2147–2162; 2001). This spacetime, in general, has non-vanishing energy flux and shear. An interesting feature of this spacetime, in contrast to other self-similar spherically symmetric spacetimes (not reducible to our form) is that it has an arbitrary radial distribution of matter. 相似文献
6.
The equation is the charged generalization of the Emden-Fowler equation that is crucial in the study of spherically symmetric shear-free spacetimes. This version arises from the Einstein–Maxwell system for a charged shear-free matter distribution. We integrate this equation and find a new first integral. For this solution to exist, two integral equations arise as integrability conditions. The integrability conditions can be transformed to nonlinear differential equations, which give explicit forms for and in terms of elementary and special functions. The explicit forms and arise as repeated roots of a fourth order polynomial. This is a new solution to the Einstein-Maxwell equations. Our result complements earlier work in neutral and charged matter showing that the complexity of a charged self-gravitating fluid is connected to the existence of a first integral. 相似文献
7.
We study shear-free spherically symmetric relativistic models with heat flow. Our analysis is based on Lie’s theory of extended
groups applied to the governing field equations. In particular, we generate a five-parameter family of transformations which
enables us to map existing solutions to new solutions. All known solutions of Einstein equations with heat flow can therefore
produce infinite families of new solutions. In addition, we provide two new classes of solutions utilising the Lie infinitesimal
generators. These solutions generate an infinite class of solutions given any one of the two unknown metric functions. 相似文献
8.
Lie symmetry method is used to perform detailed analysis on a class of KS equations. It is shown that the Lie algebra of the equation spanned by the vector fields of dilations in time and space are lost as a result of the linearity of the equation when n = 1. Symmetry reductions are carried out using each member of the optimal system. The reduced equations are further studied to obtain certain general solutions. Moreover, the conserved vectors are obtained through the application of Noether's theorem. 相似文献
9.
A. M. Msomi K. S. Govinder S. D. Maharaj 《International Journal of Theoretical Physics》2012,51(4):1290-1299
We consider a radiating shear-free spherically symmetric metric in higher dimensions. Several new solutions to the Einstein’s
equations are found systematically using the method of Lie analysis of differential equations. Using the five Lie point symmetries
of the fundamental field equation, we obtain either an implicit solution or we can reduce the governing equations to a Riccati
equation. We show that known solutions of the Einstein equations can produce infinite families of new solutions. Earlier results
in four dimensions are shown to be special cases of our generalised results. 相似文献
10.
Chandan Maji Debasis Mukherjee Dipak Kesh 《Mathematical Methods in the Applied Sciences》2020,43(7):4669-4682
This paper studies a fractional-order modelling chronic wasting disease (CWD). The basic results on existence, uniqueness, non-negativity, and boundedness of the solutions are investigated for the considered model. The criterion for local as well as global stability of the equilibrium points is derived. A numerical analysis for Hopf-type bifurcation is presented. Finally, numerical simulations are provided to justify the results obtained. 相似文献