Diffusion versus absorption in semilinear elliptic equations

We study the limit behaviour of a sequence of singular solutions of a nonlinear elliptic equation with a strongly degenerate absorption term at the boundary of the domain. We give sharp conditions on the rate of degeneracy in terms of the distance to the boundary in order the pointwise singularity not to propagate along the boundary.     

Synthesis of imatinib: a convergent approach revisited

Abstract  

A classical convergent approach for the synthesis of the anticancer drug imatinib has been substantially improved. Imatinib was assembled by coupling the amine and carboxylic acid precursors by using N,N′-carbonyldiimidazole (CDI) as a condensing agent. Both intermediates have been synthesized by novel efficient methods.     

Uniqueness classes of solutions of boundary problems for nondivergent second order parabolic equations in noncylindrical domains

In an unbounded noncylindrical domain G we consider classical solutions of general second order linear parabolic equations satisfying a Dirichlet boundary condition on the parabolic part of the boundary of G. On the basis of the maximum principle we single out classes of uniqueness of such solutions depending on the geometry of the domain G which are analogs of the classes of A. N. Tikhonov and S. Täcklind.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 7, pp. 924–930, July, 1990.     

Uniqueness classes for the solutions of the cauchy problem for nonlinear degenerate parabolic equations

Translated from Matematicheskie Zametki, Vol. 48, No. 6, pp. 118–125, December, 1990.     

The properties of volume holograms used for correction of laser beams

A theoretical study of hologram correction of laser beams is described. The result of experiments with this correction method are described for media with local response.