We study, in the radial symmetric case, the finite time life span of the compressible Euler or Euler-Poisson equations in R (N) . For time t ≥ 0, we can define a functional H(t) associated with the solution of the equations and some testing function f. When the pressure function P of the governing equations is of the form P = Kρ (γ) , where ρ is the density function, K is a constant, and γ > 1,...

Global visibility of naked singularities is analyzed here for a class of spherically symmetric spacetimes, extending previous studies limited to inhomogeneous dust cloud collapse to more physical valid situations in which pressures are non-vanishing. Existence of nonradial geodesics escaping from the singularity is shown, and the observability of the singularity from far-away observers is discu...

Classical Cepheids and RR Lyrae-type stars are usually considered to be textbook examples of purely radial, strictly periodic pulsators. Not all the variables, however, conform to this simple picture. In this review I discuss different forms of multi-periodicity observed in Cepheids and RR Lyrae stars, including Blazhko effect and various types of radial and nonradial multi-mode oscillations.

We consider a free boundary problem for a system of partial differential equations, which arise in a model of cell cycle. For the quasi steady state system, it depends on a positive parameter β, which describes the signals from the microenvironment. Upon discretizing this model, we obtain a family of polynomial systems parameterized by β. We numerically find that there exists a radially-symmetr...

has been studied by several authors, where 1 < p for N = 2, 1 < p < (N + 2)/(N − 2) for N ≥ 3 and Q(x) is a positive bounded continuous function. If Q(x) is a radial function, we can find infinity many solutions of problem (PQ) by restricting our attention to the radial functions (cf. [2, 5]). IfQ(x) is nonradial, we encounter a difficulty caused by the lack of a compact embedding of Sobolev ty...

We consider a free boundary problem for a system of partial differential equations, which arises in a model of tumor growth with a necrotic core. For any positive number R and 0 < ρ < R, there exists a radially-symmetric stationary solution with tumor free boundary r = R and necrotic free boundary r = ρ. The system depends on a positive parameter μ, which describes tumor aggressiveness, and for...