2019
Том 71
№ 4

All Issues

Shkhanukov-Lafishev M. Kh.

Articles: 4
Brief Communications (Russian)

Finite-Time Stabilization in Problems with Free Boundary for Nonlinear Equations in Media with Fractal Geometry

Berezovsky A. A., Mitropolskiy Yu. A., Shkhanukov-Lafishev M. Kh.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2005. - 57, № 7. - pp. 997–1001

By using the method of a priori estimates, we establish differential inequalities for energetic norms in $W^l_{2,r}$ of solutions of problems with a free bound in media with the fractal geometry for one-dimensional evolutionary equation. On the basis of these inequalities, we obtain estimates for the stabilization time $T$.

Article (Russian)

Stabilization for a finite time in problems with free boundary for some classes of nonlinear second-order equations

Berezansky Yu. M., Mitropolskiy Yu. A., Shkhanukov-Lafishev M. Kh.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1999. - 51, № 2. - pp. 214–223

We obtain estimates for the time of stabilization of solutions of problems with free boundary for one-dimensional quasilinear parabolic equations.

Article (Russian)

Nonlinear nonlocal problems for a parabolic equation in a two-dimensional domain

Berezovsky A. A., Mitropolskiy Yu. A., Shkhanukov-Lafishev M. Kh.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1997. - 49, № 2. - pp. 244–254

We establish the convergence of the Rothe method for a parabolic equation with nonlocal boundary conditions and obtain an a priori estimate for the constructed difference scheme in the grid norm on a ball. We prove that the suggested iterative process for the solution of the posed problem converges in the small.

Article (Russian)

Space-time localization in problems with free boundaries for a nonlinear second-order equation

Berezovsky A. A., Mitropolskiy Yu. A., Shkhanukov-Lafishev M. Kh.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1996. - 48, № 2. - pp. 202-211

For thermal and diffusion processes in active media described by nonlinear evolution equations, we study the phenomena of space localization and stabilization for finite time.