The paper is devoted to the analysis of blow-ups derivatives, gradient catastrophes and dynamics mappings $\mathbb{R}^n \to \mathbb{R}^n$ associated with $n$-dimensional homogeneous Euler equation. Several characteristic features multi-dimensional case ($n>1$) are described. Existence or nonexistence in different dimensions, boundness certain linear combinations blow-up derivatives first occurr...

A model kinetic equation is proposed to describe the time evolution of a gas composed of particles which collide inelastically. Dissipation in collisions is described by means of a parameter which is related to the coefficient of restitution, e . The kinetic equation can be solved exactly for the homogeneous cooling state, providing explicit expressions for both the time-dependent ‘‘temperature...

Abstract. The reconstruction problem for the acoustic tomography with non-homogeneous background is discussed. We develop a method of beamlike solutions of a Helmholtz equation which is not sensitive to caustics. For small perturbations of the speed the inverse scattering problem is reduced to inversion of a ray integral transform. An explicit formula is given for beam-like solutions in a homog...

unsteady flow through non - homogeneous and anisotropic porous media can be modeled by a partial differential equation.' this-equation cannot be solved analytically. hence, numerical methods. such as the finite element and the finite difference methods might be employed. in this study a mathematical model has been developed using the fully implicit finite difference method with control vol...

In this article, we discuss a recently introduced function, Ni(x), and its use in the formulation and solution of non-homogeneous Airy’s differential equation with constant forcing function. Key-words:Airy’s Functions; Scorer Functions; Non-homogeneous Airy’s ODE; Ni(x) Function.

In this study, the general partial differential equation of unsteady groundwater flow through non-homogeneous and anisotropic aquifer was solved by the fully implicit finite difference method with control volume approach. The calibration of permeability and storage coefficients as model parameters was performed by a transformation technique and application of Powell's non-linear optimization me...

the performance of water flooding can be investigated by using either detail numerical modeling or simulation, or simply through the analytical buckley-leverett (bl) model. the buckley-leverett analytical technique can be applied to one-dimensional homogeneous systems. in this paper, the impact of heterogeneity on water flooding performance and fractional flow curve is investigated. first, a ba...

platinum extraction from different secondary sources has been experimentally tested by many researchers. in this article, dissolution of platinum in aqua-regia solution from two types of spent catalysts (reforming and nitric acid production) was kinetically studied. a variety of kinetic models for heterogeneous solid-liquid reactions, including homogeneous diffusion model, shrinking core model,...

The true analogues of superspace and conformal superspace for spatially homogeneous cosmology are introduced and discussed in relation to the kinematics of the evolution of Cauchy data from a spatially homogeneous initial value surface using a spatially homogeneous lapse function. Having fixed the slicing of spatially homogeneous spacetimes to be the natural one, an obvious restriction on the f...

We investigate kinetic models of a system in contact with several spatially homogeneous thermal reservoirs at different temperatures. We explicitly find all spatially homogeneous non-equilibrium stationary states (NESS). We then consider the question of whether there are also non spatially uniform NESS. This remains partly open in general, except for a class of models to which we can apply prob...