in a finite or infinite interval ri<x<r2. Recently [2] the theory of semigroups of transformations was used to formulate the integration problem and to define the notion of lateral conditions. It will now be shown that the semi-groups constructed in [2 ] permit us to describe the totality of all stochastic processes connected with (1.1). To each there corresponds a forward, or Fokker-Planck, eq...

This article deals with finitedifference schemes of two-dimensional heat transfer equations with moving boundary. The method is suggested by solving sample problem in two-dimensional solidification of square prism. The finite-difference scheme improved for this goal is based on the Douglas equation. The results are devised for a two-dimensional model and crosschecked with results of the earlier...

−i~α · ∇w + aβw +M(x)w = f(x, |w|)w for x ∈ R3, where M(x) denotes the scaler field V (x) or V (x)β, and f describes the self-interaction which is either subcritical: W (x)|w|p−2, or critical: W1(x)|w| +W2(x)|w|, with p ∈ (2, 3). We prove multiplicity results with the number of solutions obtained depending on the ratio of minV and lim inf |x|→∞ V (x), as well as maxW and lim sup|x|→∞W (x) for t...

Implicit pressure-explicit saturation method (IMPES) is widely used in oil reservoir simulation to study the multiphase flow in porous media. This method has no complexity compared to the fully implicit method, although both of them are based on the finite difference technique. Water coning is one the most important phenomenon that affects the oil production from oil reservoirs having a water d...