On some nonlinear problems in mathematical physics with exponents close to critical ones

The paper deals with several problems having the following common feature. The differential equation under consideration contains a power function of the solution or of its gradient, with the exponent depending on a small parameter. This dependence is such that a certain property of the solutions corresponding to the positive values of the parameter may disappear as the latter tends to zero. This phenomenon is shown to be lacking in the case where not only the said exponent, but also the coefficients of the equation depend on the small parameter in a suitable way. Several theorems are proved on sharp conditions, ensuring such uniformity of various properties exhibited by the solutions. Bibliography: 44 titles. Dedicated to Olga Arsenievna Oleinik This paper has been supported in part by the Russian Foundation for Basic Research (Project 93-013-1744) and by the International Science Foundation (Grant MIE000). Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 19, pp. 000-000, 0000.     

The universal nilpotent group compactification of a semigroup

The purpose of this paper is to introduce an algebra of functions on a semitopological semigroup and to study these functions from the point of view of universal semigroup compactification. We show that the corresponding semigroup compactification of this algebra is universal with respect to the property of being a nilpotent group.

     

Numerical method for a model of inhomogeneous muscle fibers

The numerical solution of a nonlinear and nonlocal system of integro-differential equations that models the contraction of a single heterogeneous muscle fiber is studied. The method proposed is a form of the finite difference method of characteristics. Optimal error bounds are established for the resulting approximation. © 1993 John Wiley & Sons, Inc.     

Reaction of D2 with palladium fulleride C60Pd4.9

Fullerene deuteride was obtained by the reaction of deuterium with solid palladium fulleride C₆₀Pd_4.9 under fairly mild conditions. The compound was identified by FD-MS, UV-Vis and IR spectroscopies, and TLC.Translated from Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 483–484, February, 1996     

On finite element approximation and stabilization methods for compressible viscous flows

This work is devoted to the numerical solution of the Navier–Stokes equations for compressible viscous fluids. Finite element approximations and stabilization techniques are addressed. We present methods to implement discontinuous approximations for the pressure and the density. An upwinding methodology is being investigated which combines the ideas behind the stream line Petrov–Galerkin method and the flux limiter methods aiming to introduce numerical diffusion only where it is necessary.