相关论文: Asymptotic Solutions of Radiating Stars

We study a free boundary problem modelling the growth of non-necrotic tumors with fluid-like tissues. The fluid velocity satisfies Stokes equations with a source determined by the proliferation rate of tumor cells which depends on the…

We consider a relativistic radiating spherical star in conformally flat spacetimes. In particular we study the junction condition relating the radial pressure to the heat flux at the boundary of the star which is a nonlinear partial…

This paper aims at proving asymptotic stability of the radial stationary solution of a free boundary problem modeling the growth of nonnecrotic tumors with fluid-like tissues. In a previous paper we considered the case where the nutrient…

We introduce a model concerning radiational gaseous stars and establish the existence theory of stationary solutions to the free boundary problem of hydrostatic equations describing the radiative equilibrium. We also concern the local…

In this paper, we study a free boundary problem modeling solid tumor growth with vasculature which supplies nutrients to the tumor; this is characterized in the Robin boundary condition. It was recently established [Discrete Cont. Dyn.…

We have considered a stationary outflowing envelope from the star accelerated by the radiative force in arbitrary optical depth case. Introduced approximations provide satisfactory description of the behavior of the matter flux with…

We analyze the general model of a radiating star in general relativity. A group analysis of the under determined, nonlinear partial differential equation governing the model's gravitational potentials is performed. This analysis is an…

This paper studies asymptotic behavior of solutions of a free boundary problem modeling the growth of tumors with two species of cells: proliferating cells and quiecent cells. In previous literatures it has been proved that this problem has…

In this paper we study the dynamical behaviour of a simple cosmological model defined by a spatially flat Robertson-Walker geometry, conformally coupled with a massive scalar field. We determine a Lyapunov-like function for the non-linear…

We study the temporal equation of radiating stars by using three powerful methods for the analysis of nonlinear differential equations. Specifically, we investigate the global dynamics for the given master ordinary differential equation to…

We investigate the behaviour of a relativistic spherically symmetric radiative star with an accelerating, expanding and shearing interior matter distribution in the presence of anisotropic pressures. The junction condition can be written in…

In this study, we investigate the dynamics of moving fronts in three-dimensional spaces, which form as a result of in-situ combustion during oil production. This phenomenon is also observed in other contexts, such as various autowave models…

We study the asymptotic diffusion processes with (generally nonlocal) open boundaries in one dimension which are exactly solvable by means of the recently developed recursion formula. We investigate the stationary states, which cannot be…

Motivated by the stellar wind ejected from the upper atmosphere (Corona) of a star, we explore a boundary problem of the two-species nonlinear relativistic Vlasov-Poisson systems in the 3D half space in the presence of a constant vertical…

This paper studies the boundary behaviour at mechanical equilibrium at the ends of a finite interval of a class of systems of interacting particles with monotone decreasing repulsive force. Our setting covers pile-ups of dislocations,…

Stationary solutions to the equations of non-linear diffusive shock acceleration play a fundamental role in the theory of cosmic-ray acceleration. Their existence usually requires that a fraction of the accelerated particles be allowed to…

For a singularly perturbed system of reaction--diffusion equations, assuming that the 0th order solutions in regular and singular regions are all stable, we construct matched asymptotic expansions for formal solutions to any desired order…

In this paper we study a free boundary problem modeling the growth of solid tumor spheroid. It consists of two elliptic equations describing nutrient diffusion and pressure distribution within tumor, respectively. The new feature is that…

We propose a new method to study the quasi-normal modes of rotating relativistic stars. Oscillations are treated as perturbations in the frequency domain of the stationary, axisymmetric background describing a rotating star. The perturbed…

We investigate avascular tumour growth as a two-phase process consisting of cells and liquid. Based on the one-dimensional continuum moving-boundary model formulated by (Byrne, King, McElwain, Preziosi, Applied Mathematics Letters, 2003,…