Khruslov E. Ya.
Ukr. Mat. Zh. - 2019. - 71, № 5. - pp. 692-705
UDC 517.95, 519.21
We consider a boundary-value problem for the equation of stationary diffusion in a porous medium filled with small ball inclusions with absorbing surfaces. Absorption is described by a Robin’s nonlinear boundary condition. The locations and radii of the inclusions are randomly distributed and described by a set of finite-dimensional distribution functions. We study the asymptotic behavior of solutions to the problem when the number of balls increases and their radii decrease. We derive a homogenized equation for the main term of the asymptotics, and determine sufficient conditions for the distribution functions under which the solutions converge to the solutions of the homogenized problem in probability.
Antoniouk A. Vict., Berezansky Yu. M., Boichuk О. A., Gutlyanskii V. Ya., Khruslov E. Ya., Kochubei A. N., Korolyuk V. S., Kushnir R. M., Lukovsky I. O., Makarov V. L., Marchenko V. O., Nikitin A. G., Parasyuk I. O., Pastur L. A., Perestyuk N. A., Portenko N. I., Ronto M. I., Sharkovsky O. M., Tkachenko V. I., Trofimchuk S. I.
Ukr. Mat. Zh. - 2018. - 70, № 1. - pp. 3-6
Boichuk О. A., Gorbachuk M. L., Gorodnii M. F., Khruslov E. Ya., Lukovsky I. O., Makarov V. L., Parasyuk I. O., Samoilenko A. M., Samoilenko V. G., Sharkovsky O. M., Shevchuk I. A., Slyusarchuk V. Yu., Stanzhitskii A. N.
Ukr. Mat. Zh. - 2016. - 68, № 1. - pp. 142-144
Regularized integrals of motion for the Korteweg – de-Vries equation in the class of nondecreasing functions
Ukr. Mat. Zh. - 2015. - 67, № 12. - pp. 1587-1601
We study the Cauchy problem for the Korteweg–de-Vries equation in the class of functions approaching a finite- zone periodic solution of the KdV equation as $x → −∞$ and 0 as $x → +∞$. We prove the existence of infinitely many “regularized” integrals of motion for the solutions $u(x, t)$ of the Cauchy problem, with explicit dependence on time.
Ukr. Mat. Zh. - 2013. - 65, № 3. - pp. 451-454
Ukr. Mat. Zh. - 2013. - 65, № 2. - pp. 192-225
We consider a coupled system of the Navier- Stokes and Fokker- Planck equations that describes the motion of a polydisperse suspension of solid particles in a viscous incompressible liquid. We prove the existence theorem and study some properties of global weak solutions of the initial boundary-value problem for this system.
Ukr. Mat. Zh. - 2011. - 63, № 11. - pp. 1443-1459
We consider a homogenized system of equations that is a macroscopic model of nonstationary vibrations of an elastic medium with a large number of small cavities filled with viscous incompressible liquid (wet elastic medium). It is proved that the solution of the initial boundary-value problem for this system in a bounded domain $\Omega$ tends to zero in the metric of $L_2(\Omega)$ exponentially with time.
Ukr. Mat. Zh. - 2010. - 62, № 10. - pp. 1309–1329
We consider an initial boundary-value problem used to describe the nonstationary vibration of an elastic medium with large number of small cavities filled with a viscous incompressible fluid. We study the asymptotic behavior of the solution in the case where the diameters of the cavities tend to zero, their number tends to infinity, and the cavities occupy a three-dimensional region. We construct an averaged equation to describe the leading term of the asymptotics. This equation serves as a model of propagation of waves in various media, such as damped soil, rocks, and some biological tissues.
Adamyan V. M., Berezansky Yu. M., Khruslov E. Ya., Kochubei A. N., Kuzhel' S. A., Marchenko V. O., Mikhailets V. A., Nizhnik L. P., Ptashnik B. I., Rofe-Beketov F. S., Samoilenko A. M., Samoilenko Yu. S.
Ukr. Mat. Zh. - 2008. - 60, № 4. - pp. 439–442
Ukr. Mat. Zh. - 2007. - 59, № 12. - pp. 1699-1700
Ukr. Mat. Zh. - 2005. - 57, № 8. - pp. 1120-1122
Ukr. Mat. Zh. - 2004. - 56, № 3. - pp. 291-292
Ukr. Mat. Zh. - 2001. - 53, № 3. - pp. 291-293
Berezansky Yu. M., Kharlamov P. V., Khruslov E. Ya., Kit G. S., Korneichuk N. P., Korolyuk V. S., Kovalev A. M., Kovalevskii A. A., Lukovsky I. O., Mitropolskiy Yu. A., Samoilenko A. M., Savchenko O. Ya.
Ukr. Mat. Zh. - 2000. - 52, № 11. - pp. 1443-1445