Related papers: Self-similar spherical shock solution with sustain…
In this study we obtain the solution of the spherically symmetric de Sitter solution of black holes using a general form of distribution functions which include Gaussian, Rayleigh, and Maxwell-Boltzmann distribution as a special case. We…
We present a self-similar solution to describe the propagation of a shock wave whose energy is deposited or lost at the front. Both of the propagation of the shock wave in a medium having a power-law density profile and the expansion of the…
We prove a constructive stable ODE-type blowup result for open sets of solutions to a family of quasilinear wave equations in three spatial dimensions featuring a Riccati-type derivative-quadratic semilinear term. The singularity is more…
We present a dark fluid model which contains the general linear equation of state including the gravitation term. The obtained spherical symmetric Euler equation and the continuity equation was investigated with the Sedov-type…
A particular choice of the time function in the recently presented spherical solution by Dadhich [1] leads to a singularity free cosmological model which oscillates between two regular states. The energy-stress tensor involves anisotropic…
Similarity solutions play an important role in many fields of science: we consider here similarity in stochastic dynamics. Important issues are not only the existence of stochastic similarity, but also whether a similarity solution is…
We study exact solutions for the slow viscous flow of an infinite liquid caused by two rigid spheres approaching each either along or parallel to their line of centres, valid at all separations. This goes beyond the applicable range of…
We construct axisymmetric self-similar solutions of transonic outflows emanating from a point source including the effect of the rotation. The solutions are constructed exclusively on the equatorial plane. The features of solutions are…
We consider a strong ultrarelativistic shock moving through a star whose envelope has a polytrope-like density profile. When the shock is close to the star's outer boundary, its behavior follows the self-similar solution given by Sari…
Existence, uniqueness and stability of solutions is studied for a set of nonlinear fixed point equations which define self-consistent hydrostatic equilibria of a classical continuum fluid that is confined inside a container and in contact…
This paper is devoted to a fundamental solution of a nonlinear kinetic equation involving a porous medium or fast diffusion operator acting on velocities. Such a nonlinearity has interesting scaling properties, which result in a…
Stability of self-similar solutions for gravitational collapse is an important problem to be investigated from the perspectives of their nature as an attractor, critical phenomena and instability of a naked singularity. In this paper we…
We present the results of three-dimensional special relativistic hydrodynamic simulations of supernova ejecta with a powerful central energy source. We assume spherical supernova ejecta freely expanding with the initial kinetic energy of…
Analytical modeling of the evolution of cylindrical and spherical shock waves (shocks) during an implosion in water is presented for an intermediate range of convergence radii. Up to now this range is determined only in experiments…
A sufficiently powerful astrophysical source with power law luminosity in time will give rise to a self-similar relativistic blast wave with a reverse shock traveling into the ejecta and a forward shock moving into the surrounding medium.…
We address the existence and stability of transonic shocks for the two-dimensional steady rotating Euler system in an almost flat nozzle. Under the influence of the Coriolis force, we first establish a class of special transonic shock…
I study a class of global, causal geodesically complete solutions to the spherically symmetric Einstein scalar field (SSESF) system . Extending results of Luk-Oh (Quantitative Decay Rates for Dispersive Solutions to the Einstein-Scalar…
The hydrodynamics of an ultrarelativistic flow, enclosed by a strong shock wave, are described by the well known Blandford-McKee solutions in spherical geometry. These solutions, however, become inaccurate at a distance $\sim R/2$ behind…
We consider shock reflection which has a well-known local non-uniqueness: the reflected shock can be either of two choices, called weak and strong. We consider cases where existence of a global solution with weak reflected shock has been…
We prove the existence of self-similar fundamental solutions (SSF) of the anisotropic porous medium equation in the suitable fast diffusion range. Each of such SSF solutions is uniquely determined by its mass. We also obtain the asymptotic…