List of publications

## Monographs

- Усредненные модели динамики суспензий. — Киев: Наукова Думка (2016), 340с.
- Homogenization of Partial Differential Equations. Progress in Mathematical Physics. — Boston: Birkhäuser Boston, Inc., MA (2006), 398 p. (with V.A. Marchenko).
- Усредненные модели микронеоднородных сред. — Киев: Наук. думка (2005), 550 с. (with V.A. Marchenko).
- Boundary value problems in domains with a fine-grained boundary. (Russian) — "Naukova Dumka'', Kiev (1974), 279 pp. (with V.A. Marchenko).

## Publications in refereed Journals and Proceedings

- Nonlinear Dynamics of Solitons for the Vector Modified Korteweg-de Vries Equation. Zh. Mat. Fiz. Anal. Geom. 14 (2018), no. 2, pp. 153-168 (with Fenchenko, V.).
- Integral conditions for convergence of solutions of non-linear Robin's problem in strongly perforated domain. Zh. Mat. Fiz. Anal. Geom. 13 (2017), no. 3, 283–313. (with Khilkova, L. O.; Goncharenko, M. V.)
- Regularized integrals of motion of the Korteweg–de Vries equation in a class of nondecreasing functions. (Russian) Ukraïn. Mat. Zh. 67 (2015), no. 12, 1587-1601; translation in Ukrainian Math. J. 67 (2016), no. 12, 1793–1809 (with Andreev, K. N.).
- A homogenized model of the small oscillations of an elastic system of masses with nonlocal interaction. (Russian) Dopov. Nats. Akad. Nauk Ukr. Mat. Prirodozn. Tekh. Nauki 2015, no. 10, 12–16 (with Berezhnoĭ, M. and Radyakin, N. K.).
- Gaps in the spectrum of the Neumann Laplacian generated by a system of periodically distributed traps. Math. Methods Appl. Sci. 38 (2015), no. 1, 11–26 (with Khrabustovskyi, Andrii).
- Global weak solutions of the Navier-Stokes/Fokker-Planck/Poisson linked equations. Zh. Mat. Fiz. Anal. Geom. 10 (2014), no. 3, 267–299 (Anoshchenko, O. and Iegorov, S.).
- Homogenized model of oscillations of elastic medium with small caverns filled with viscous incompressible fluid. Spectral theory and differential equations, 179–197, Amer. Math. Soc. Transl. Ser. 2, 233, Adv. Math. Sci., 66, Amer. Math. Soc., Providence, RI, 2014 (with Goncharenko, M. V. and Radyakin, N. K.).
- Preface. Spectral theory and differential equations, ix–x, Amer. Math. Soc. Transl. Ser. 2, 233, Adv. Math. Sci., 66, Amer. Math. Soc., Providence, RI, 2014 (with Pastur, L. and Shepelsky, D.).
- Asymptotic behavior of a suspension of oriented particles in a viscous incompressible fluid. Asymptot. Anal. 83 (2013), no. 4, 331–353 (with Berezhnyi, M.).
- Global weak solutions of the Navier-Stokes-Fokker-Planck system. Translation of Ukraïn. Mat. Zh. 65 (2013), no. 2, 192–225. Ukrainian Math. J. 65 (2013), no. 2, 212–248 (with Egorov, S. M.).
- On the exponential decay of vibrations of damped elastic media. Ukrainian Math. J. 63 (2012), no. 11, 1641–1659 (with Goncharenko, M. V.).
- Asymmetric hydrodynamics of suspensions subjected to the influence of strong external magnetic fields. J. Multiscale Model. 4 (2012), no. 1, 1250002, 22 pp (with Berezhnyi, M.).
- Averaged model of vibration of a damped elastic medium. Ukrainian Math. J. 62 (2011), no. 10, 1519–1542; translated from Ukraïn. Mat. Zh. 62 (2010), no. 10, 1309-1329 (Russian) (with Goncharenko, M. V.)
- Non-standard dynamics of elastic composites. Netw. Heterog. Media 6 (2011), no. 1, 89–109 (Berezhnyi, M.).
- Global weak solutions to the Navier-Stokes-Vlasov-Poisson system. Zh. Mat. Fiz. Anal. Geom. 6 (2010), no. 2, 143–182, 247, 249 (Anoshchenko, O.; Stephan, H.).
- On convergence of solutions of singularly perturbed boundary-value problems. Zh. Mat. Fiz. Anal. Geom. 5 (2009), no. 2, 115–122, 213 (Anoshchenko, O. and Lysenko, O.).
- The homogenized model of small oscillations of complex fluids. Netw. Heterog. Media 3 (2008), no. 4, 831–862 (Berezhnyi, M. and Berlyand, L.).
- Homogenization of Maxwell's equations in domains with dense perfectly conducting grids. Ukr. Mat. Visn. 2 (2005), no. 1, 109-142; translation in Ukr. Math. Bull. 2 (2005), no. 1, 113–145.
- Ginzburg-Landau model of a liquid crystal with random inclusions. J. Math. Phys. 46 (2005), no. 9, 095107, 15 pp (with Berlyand, L.).
- Homogenized non-Newtonian viscoelastic rheology of a suspension of interacting particles in a viscous Newtonian fluid. SIAM J. Appl. Math. 64 (2004), no. 3, 1002–1034 (with Berlyand, L.).
- Generation of asymptotic solitons in an integrable model of stimulated Raman scattering by periodic boundary data. Mat. Fiz. Anal. Geom. 10 (2003), no. 3, 366–384 (with Kotlyarov, V.).
- Competition between the surface and the boundary layer energies in a Ginzburg-Landau model of a liquid crystal composite. Asymptot. Anal. 29 (2002), no. 3-4, 185–219 (with Berlyand, L.).
- Soliton asymptotics of rear part of non-localized solutions of the Kadomtsev-Petviashvili equation. J. Nonlinear Math. Phys. 9 (2002), no. 1, 58–76 (with Boutet de Monvel, A. and Kotlyarov, V.).
- Homogenization of harmonic maps with large number of vortices and applications in superconductivity and superfluidity. Adv. Differential Equations 6 (2001), no. 2, 229–256 (with Berlyand, L.).
- Averaging of Maxwell equations on manifolds of complicated microstructure. (Russian) Mat. Fiz. Anal. Geom. 7 (2000), no. 1, 91–114 (with Palʹ-Valʹ, A. P.).
- Homogenization of the Dirichlet variational problems in Orlicz-Sobolev spaces. Operator theory and its applications (Winnipeg, MB, 1998), 345–366, Fields Inst. Commun., 25, Amer. Math. Soc., Providence, RI, 2000 (with Pankratov, L. S.).
- Homogenization of harmonic 1-forms on Riemannian surfaces of increasing genus. Dopov. Nats. Akad. Nauk Ukr. Mat. Prirodozn. Tekh. Nauki 1999, no. 2, 39–43 (with Pal-Val, A. P.).
- Homogenization of harmonic maps and superconducting composites. SIAM J. Appl. Math. 59 (1999), no. 5, 1892–1916 (with Berlyand, L.).
- Homogenization of harmonic vector fields on Riemannian manifolds with complicated microstructure. Math. Phys. Anal. Geom. 1 (1998), no. 1, 1–22 (with Boutet de Monvel, L.).
- The Cauchy problem for the sinh-Gordon equation and regular solitons. Inverse Problems 14 (1998), no. 6, 1403–1427 (with Boutet de Monvel, A. and Kotlyarov, V.).
- Splitting of some non-localized solutions of the Korteweg-de Vries equation into solitons. Mat. Fiz. Anal. Geom. 5 (1998), no. 1-2, 49–67 (with Stephan, H.).
- Homogenization of attractors for semilinear parabolic equations on manifolds with complicated microstructure. Ann. Mat. Pura Appl. (4) 172 (1997), 297–322 (with Boutet de Monvel, L. and Chueshov, I. D.).
- Soliton asymptotics of non-localized solutions of non-linear evolutionary equations. Proceedings of the Second World Congress of Nonlinear Analysts, Part 7 (Athens, 1996). Nonlinear Anal. 30 (1997), no. 7, 3951–3961 (with Anders, I. A. and Kotlyarov, V. P.).
- Averaging of the Neumann problem for higher-order elliptic operators. (Russian) Dopov. Nats. Akad. Nauk Ukr. Mat. Prirodozn. Tekh. Nauki 1997, no. 4, 43–47 (with Vorobʹeva, G. I.).
- Averaging of a diffusion equation on Riemannian manifolds of complex microstructure. (Russian) Tr. Mosk. Mat. Obs. 58 (1997), 158-186; translation in Trans. Moscow Math. Soc. 1997, 137–161 (with Boutet de Monvel, L.).
- Soliton asymptotics of the Cauchy problem solution for the Toda lattice. Inverse Problems 13 (1997), no. 2, 223–237 (with Boutet de Monvel, A. and Egorova, I.).
- Uniform asymptotic formulas for curvilinear solitons of the Kadomtsev-Petviashvili equations. (Russian) Teoret. Mat. Fiz. 108 (1996), no. 2, 205-211; translation in Theoret. and Math. Phys. 108 (1996), no. 2, 1013–1018 (1997) (with Ostapenko, D. Yu. and Palʹ-Valʹ, A. P.).
- Soliton asymptotics of non-decreasing solutions of nonlinear evolutionary equations. Algebraic and geometric methods in mathematical physics (Kaciveli, 1993), 307–322, Math. Phys. Stud., 19, Kluwer Acad. Publ., Dordrecht, 1996.
- Homogenization of electrostatic problems in domains with nets. Homogenization and applications to material sciences (Nice, 1995), 215–223, GAKUTO Internat. Ser. Math. Sci. Appl., 9, Gakkōtosho, Tokyo, 1995 (with Goncharenko, M.).
- Homogenized models of strongly inhomogeneous media. Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Zürich, 1994), 1270–1278, Birkhäuser, Basel, 1995.
- Bute de Monvelʹ, L.; Khruslov, E. Ya. An averaged model of the diffusion of colored particles in domains with small obstacles. (Russian) Mat. Fiz. Anal. Geom. 1 (1994), no. 1, 78–101.
- Curved asymptotic solitons of the Kadomtsev-Petviashvili equation. (Russian) Teoret. Mat. Fiz. 99 (1994), no. 1, 27-35; translation in Theoret. and Math. Phys. 99 (1994), no. 1, 402–408 (with Anders, I. A. and Kotlyarov, V. P.).
- Homogenization of boundary problems for the Ginzburg-Landau equation in weakly connected domains. Spectral operator theory and related topics, 233–268, Adv. Soviet Math., 19, Amer. Math. Soc., Providence, RI, 1994 (with Pankratov, L.).
- Soliton asymptotics of nondecreasing solutions of nonlinear completely integrable evolution equations. Spectral operator theory and related topics, 129–180, Adv. Soviet Math., 19, Amer. Math. Soc., Providence, RI, 1994 (with Kotlyarov, V. P.).
- Inverse scattering method in electromagnetic sounding theory. Inverse Problems 10 (1994), no. 1, 1–37 (with Shepelsky, D. G.).
- Inverse problems of magnetotelluric sounding in the case of horizontal propagation of generating waves. (Russian) Izv. Akad. Nauk SSSR Ser. Fiz. Zemli 1991, no. 12, 73–83 (with Levchenko, E. P.).
- Homogenized models of composite media. Composite media and homogenization theory (Trieste, 1990), 159–182, Progr. Nonlinear Differential Equations Appl., 5, Birkhäuser Boston, Boston, MA, 1991.
- Asymptotic behavior of solutions of variational problems in domains with a fine-grained boundary. (Russian) Dokl. Akad. Nauk Ukrain. SSR Ser. A 1990, no. 2, 20–22, 84 (with Pankratov, L. S.).
- An averaged model of a strongly inhomogeneous medium with memory. (Russian) Uspekhi Mat. Nauk 45 (1990), no. 1(271), 197-198; translation in Russian Math. Surveys 45 (1990), no. 1, 211–212.
- Matrix generalisation of the modified Korteweg-de Vries equation. Inverse Problems 6 (1990), no. 2, 193–204 (with Khalilov, F. A.).
- Khruslov, Ē. Ya. Asymptotic behavior of solutions of the second boundary value problem in domains with random thin cracks. (Russian) Teor. Funktsiĭ Funktsional. Anal. i Prilozhen. No. 52 (1989), 91-103; translation in J. Soviet Math. 52 (1990), no. 5, 3412–3421 (with Egorova, I. E.).
- Averaged models of diffusion in fractured-porous media. (Russian) Dokl. Akad. Nauk SSSR 309 (1989), no. 2, 332-335; translation in Soviet Phys. Dokl. 34 (1989), no. 11, 980–981 (1990).
- Asymptotic solitons of the modified Korteweg-de Vries equation. Inverse Problems 5 (1989), no. 6, 1075–1088 (with Kotlyarov, V. P.).
- Asymptotic solitons. (Russian) Functional and numerical methods in mathematical physics (Russian), 103–107, 267, "Naukova Dumka'', Kiev, 1988 (with Kotlyarov, V. P.).
- Solvability in the large of a problem that describes the motion of the suspension of rigid axisymmetric particles in a viscous fluid. (Russian) Vestnik Kharʹkov. Gos. Univ. No. 315, Upravl. Sistemy (1988), 105–110 (with Lʹvov, V. A.).
- Matrix generalization of the modified Korteweg-de Vries equation. (Russian) Mathematical physics, functional analysis (Russian), 3–17, 143, "Naukova Dumka'', Kiev, 1986 (with Khalilov, F. A.).
- Time asymptotics of the solution of the Cauchy problem for the modified Korteweg-de Vries equation with nondecreasing initial data. (Russian) Dokl. Akad. Nauk Ukrain. SSR Ser. A 1986, no. 10, 61–64 (with Kotlyarov, V. P.).
- Solitons of the nonlinear Schrödinger equation, which are generated by the continuous spectrum. (Russian) Teoret. Mat. Fiz. 68 (1986), no. 2, 172–186 (Kotlyarov, V. P.).
- One-dimensional inverse problems of electrodynamics. (Russian) Zh. Vychisl. Mat. i Mat. Fiz. 25 (1985), no. 4, 548–561, 638.
- An inverse scattering problem for an equation of electric geophysical exploration. (Russian) General theory of boundary value problems, 213–219, "Naukova Dumka'', Kiev, 1983.
- Convergence of solutions of the second boundary value problem in weakly connected domains. (Russian) Theory of operators in function spaces and its applications, pp. 129–173, 191, "Naukova Dumka'', Kiev, 1981.
- Asymptotic behavior of solutions of differential equations with a strongly oscillating coefficient matrix that does not satisfy a uniform boundedness condition. (Russian) Dokl. Akad. Nauk Ukrain. SSR Ser. A 1981, no. 4, 24–27, 95 (with Fenchenko, V. N.).
- Asymptotic behavior of the solutions of differential equations with strongly oscillating and degenerating coefficient matrix. (Russian) Dokl. Akad. Nauk Ukrain. SSR Ser. A 1980, no. 4, 26–30, 99 (with Fenčenko, V. N.).
- Perturbation of the thermal field of moving small particles. (Russian) Studies in the theory of operators and their applications (Russian), pp. 49–65, 177, "Naukova Dumka'', Kiev, 1979 (with Nazyrov, Z. F.).
- Perturbation of a viscous incompressible fluid by small particles. (Russian) Theoretical and applied questions of differential equations and algebra (Russian), pp. 173–177, 267, "Naukova Dumka'', Kiev, 1978 (with Lʹvov, V. A.).
- Asymptotic behavior of the solutions of the second boundary value problem in the case of the refinement of the boundary of the domain. (Russian) Mat. Sb. 106(148) (1978), no. 4, 604–621.
- The first boundary value problem in domains with a complex boundary for higher order equations. (Russian) Mat. Sb. (N.S.) 103(145) (1977), no. 4, 614–629, 632.
- Estimation of the accuracy of approximation of solutions of boundary value problems with a fine-grained boundary. (Russian) Problems in mechanics and mathematical physics (Russian), pp. 208–223, 298. Izdat. "Nauka'', Moscow, 1976 (with Marchenko, V. A.).
- Asymptotic behavior of the solution of the Cauchy problem for the Korteweg-de Vries equation with steplike initial data. (Russian) Mat. Sb. (N.S.) 99(141) (1976), no. 2, 261–281, 296.
- Boundary value problems in domains with a fine-grained boundary for the general system of Navier-Stokes equations. (Russian) Vestnik Harʹkov. Gos. Univ. No. 119 Mat. i Meh. Vyp. 40 (1975), 23–36, i (with Lʹvov, V. A.).
- Boundary value problems in domains with a fine-grained boundary for the linearized system of Navier-Stokes equations. (Russian) Vestnik Harʹkov. Gos. Univ. No. 119 Mat. i Meh. Vyp. 40 (1975), 3–22, i (with Lʹvov, V. A.).
- The equations of an elastic medium with a large number of small perfectly solid insertions. (Ukrainian) Dopovīdī Akad. Nauk Ukraïn. RSR Ser. A 1973, 500–503, 572 (with Kotljarov, V. P.).
- The equations of an elastic medium with a large number of small absolutely rigid insertions. (Russian) Mat. Fiz. i Funkcional. Anal. Vyp. 3 (1972), 39–51, 108 (with Kotljarov, V. P.).
- The method of orthogonal projections and the Dirichlet boundary value problem in domains with a "fine-grained'' boundary. (Russian) Mat. Sb. (N.S.) 88(130) (1972), 38–60.
- The measure connected with a sequence of solutions of first boundary value problems. (Russian) Teor. Funkciĭ Funkcional. Anal. i Priložen. No. 16 (1972), 29–38, 216.
- The first boundary value problem for an elliptic selfadjoint operator in a domain with a fine-grained boundary. (Ukrainian) Dopovīdī Akad. Nauk Ukraïn. RSR Ser. A. 1972, 343–345, 382.
- The second boundary value problem of linear elasticity theory in domains with a fine-grained boundary. (Ukrainian) Dopovīdī Akad. Nauk Ukraïn. RSR Ser. A 1972, 415–418, 477 (with Kotljarov, V. P.).
- A study of the solution of the second boundary value problem in a domain with a boundary that consists of a large number of perforated surfaces. (Russian) Mat. Fiz. i Funkcional. Anal. Vyp. 2 (1971), 76–98, 237 (with Lʹvov, V. A.).
- The limit boundary condition of a certain Neumann problem. (Russian) Teor. Funkciĭ Funkcional. Anal. i Priložen. No. 10 (1970), 83–96 (with Kotljarov, V. P.).
- Conditions for the convergence of a sequence of solutions of the first boundary value problem. (Russian) Teor. Funkciĭ Funkcional. Anal. i Priložen. No. 12 (1970), 103–110.
- The Dirichlet problem in a region with a random boundary. (Russian) Vestnik Harʹkov. Gos. Univ. No. 53 1970 14–37.
- The Neumann boundary value problem in a domain with a composite boundary. (Russian) Mat. Sb. (N.S.) 83 (125) 1970 556–574.
- The resonance phenomena in a certain diffraction problem. (Russian) Teor. Funkciĭ Funkcional. Anal. i Priložen. Vyp. 6 1968 111–129.
- The passage of sound waves across thin channels in a reflecting layer. (Russian) Teor. Funkciĭ Funkcional. Anal. i Priložen. Vyp. 5 1967 140–156 (with Suzikov, G. V.).
- An averaged boundary condition for a diffusion problem in a region with piecewise semipermeable boundary. (Russian) Teor. Funkciĭ Funkcional. Anal. i Priložen. Vyp. 4 1967 146–161 (with Suzikov, G. V.).
- First boundary value problem in regions with a composite boundary. (Russian) Vestnik Harʹkov. Gos. Univ. 1966 1966 no. 14, 3–16.
- Investigation of the limiting case of the first boundary value problem. (Russian) Teor. Funkciĭ Funkcional. Anal. i Priložen. Vyp. 1 1965 71–87.
- Analytical properties of the resolvent of a boundary value problem. (Russian) 1965 First Republ. Math. Conf. of Young Researchers, Part I (Russian) pp. 677–683 Akad. Nauk Ukrain. SSR Inst. Mat., Kiev.
- Boundary-value problems with fine-grained boundary. (Russian) Mat. Sb. (N.S.) 65 (107) 1964 458–472. (with Marchenko, V. A.)