On one problem with free boundary for a nonlinear system

We formulate the filtration problem with free boundary as a problem with discontinuous nonlinearity for a degenerate elliptic or parabolic system. We prove that a solution of the Dirichlet problem exists in both cases. We study some qualitative properties of these solutions, e.g., the existence of “dead cores”. Institute of Applied Mathematics and Mechanics, Ukrainian Academy of Sciences, Donetsk. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 48, No. 9, pp. 1155–1165, September, 1996.     

Classical Solvability of the First Initial Boundary-Value Problem for a Nonlinear Strongly Degenerate Parabolic Equation

We prove the existence of a classical solution global in time for the first initial boundary-value problem for a nonlinear strongly degenerate parabolic equation.__________Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 10, pp. 1299 – 1320, October, 2004.     

ω-(2-benzimidazolyl)perfluorinated carboxylic acids and their derivatives

A convenient method is proposed for the preparation of -(2-benzimidazolyl) perfluorinated carboxylic acids and their amides by condensation of o-phenylenediamine with imides of perfluorinated dicarboxylic acids. The transformations of the o-aminoanilides of the amides of the perfluorinated dicarboxylic acids were studied by thermal analysis and mass spectroscopy.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 9, pp. 1262–1265, September, 1976.     

The Cauchy Problem for the Fractional Diffusion Equation in a Weighted Hölder Space

Under study is the Cauchy problem for the fractional diffusion equation with a Caputo derivative. The existence and uniqueness theorems for a smooth solution are proven in a weighted H¨older space.     

Reactions of hydrazine derivatives

On the basis of a combined study of chemical properties and UV, IR, PMR, and mass spectra, it has been shown that the product of the transformation of 3,4-tetramethylene-5, 5-pentamethylenepyrazoline under the action of sulfur has the structure of 3-pentyl-4,5,6,7-tetrahydroindazole.For part XLIV, see [1].