2019
Том 71
№ 10

# Khruslov E. Ya.

Articles: 14
Article (Russian)

### Model of stationary diffusion with absorption in domains with fine-grained random boundaries

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.

Anniversaries (Ukrainian)

### Anatolii Mykhailovych Samoilenko (on his 80th birthday)

Ukr. Mat. Zh. - 2018. - 70, № 1. - pp. 3-6

Anniversaries (Ukrainian)

### Mykola Oleksiiovych Perestyuk (on his 70th birthday)

Ukr. Mat. Zh. - 2016. - 68, № 1. - pp. 142-144

Article (Russian)

### 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.

Anniversaries (Ukrainian)

### Myroslav L’vovych Horbachuk (on his 75 th birthday)

Ukr. Mat. Zh. - 2013. - 65, № 3. - pp. 451-454

Article (Russian)

### Global weak solutions of the Navier?Stokes?Fokker?Planck system

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.

Article (Russian)

### On the exponential decay of vibrations of damped elastic media

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.

Article (Russian)

### Averaged model of vibration of a damped elastic medium

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.

Article (Ukrainian)

### Myroslav L’vovych Horbachuk (on his 70th birthday)

Ukr. Mat. Zh. - 2008. - 60, № 4. - pp. 439–442

Anniversaries (Ukrainian)

### Leonіd Andrіyovich Pastur (on his 70th birthday)

Ukr. Mat. Zh. - 2007. - 59, № 12. - pp. 1699-1700

Anniversaries (Ukrainian)

### Leonid Pavlovych Nyzhnyk (on his 70-th birthday)

Ukr. Mat. Zh. - 2005. - 57, № 8. - pp. 1120-1122

Anniversaries (Ukrainian)

### Dmytro Yakovych Petryna (on his 70 th birthday)

Ukr. Mat. Zh. - 2004. - 56, № 3. - pp. 291-292

Anniversaries (Russian)

### Naum Il'ich Akhiezer (on his 100-th birthday)

Ukr. Mat. Zh. - 2001. - 53, № 3. - pp. 291-293

Anniversaries (Ukrainian)

### Igor Volodymyrovych Skrypnik (On His 60th Birthday)

Ukr. Mat. Zh. - 2000. - 52, № 11. - pp. 1443-1445