Radiating Collapse with Vanishing Weyl stresses

In a recent approach in modelling a radiating relativistic star undergoing gravitational collapse the role of the Weyl stresses was emphasised. It is possible to generate a model which is physically reasonable by approximately solving the junction conditions at the boundary of the star. In this paper we demonstrate that it is possible to solve the Einstein field equations and the junction conditions exactly. This exact solution contains the Friedmann dust solution as a limiting case. We briefly consider the radiative transfer within the framework of extended irreversible thermodynamics and show that relaxational effects significantly alter the temperature profiles.Comment: 10 pages, submitted to IJMP-

Optimal error estimates of a mixed finite element method for\ud parabolic integro-differential equations with non smooth initial data

In this article, a new mixed method is proposed and analyzed for parabolic integro-differential equations (PIDE) with nonsmooth initial data. Compared to mixed methods for PIDE, the present method does not bank on a reformulation using a resolvent operator. Based on energy arguments and without using parabolic type duality technique, optimal L2-error estimates are derived for semidiscrete approximations, when the initial data is in L2. Due to the presence of the integral term, it is, further, observed that estimate in dual of H(div)-space plays a role in our error analysis. Moreover, the proposed analysis follows the spirit of the proof technique used for deriving optimal error estimates of finite element approximations to PIDE with smooth data and therefore, it unifies both the theories, i.e., one for smooth data and other for nonsmooth data. Finally, the proposed analysis can be easily extended to other mixed method for PIDE with rough initial data and provides an improved result