Dr.Sc.  Belarus Polytechnic Academy
Minsk, Belarus 
1992  Mechanical Engineering 
Ph.D.  Belarus State University
Minsk, Belarus 
1978  Applied Mathematics 
Extensive experience in applied mathematics, solid, and fluid mechanics. Combination of strong theoretical background and mathematical simulation skills. Fields of activity include mathematical modeling of physical phenomena in solid mechanics, dynamic fracture mechanics, and two phase flow of incompressible fluid. Intensive applications of boundary element methods, finite element methods, and finite difference methods. Regularization and numerical calculation of singular and hypersingular integrals. Solid background in statistics. Good computer programming skills (Fortran, C/C++, PowerBuilder, and Matlab), UNIX experience (on SUN and SGI platform), and proficient in Windows applications (Word, Excel, Excess) and Software tools (HTML, Minitab, SAS, R, LaTeX, CASs). 
Partial Differential Equations Wave equations with oblique boundary conditions: 

Scalar wave propagation problems with the Dirichlet or Neumann boundary conditions have been extensively studied. The mixed problem for the wave equation with an oblique derivative is illposed. The conditions of normal solvability were found. The exact solutions of initial value problems for wave equation have been constructed. Main publications: Dobrushkin, V.A. (1994). On solvability of mixed problem in a domain with an angle for wave equation. Sib. J. Diff. Equations, 3, No. 2, 3  10 (1994). 

Shock problems:  
The shock phenomena in solid mechanics is simulated as an initialboundary value problem for PDE with discontinuous initial data. A rigorous solution of such problem was obtained and the uniqueness theorem was proved. Main publications: Dobrushkin, V.A., & Gaiduk, S.I. (1979). Solution of a problem in the theory of thermoelasticity related to mechanical and thermal shocks. English transl. in Differential equations, 15, 1165  1174; Dobrushkin, V.A. (1977). The uniqueness of the generalized solution of a certain problem in shock theory. English transl. in Differential Equations, 13 , 1061  1063. 

Resolvent method in abstract differentialoperator equations and elastodynamics:  
A new method for solving linear boundary value problems for abstract operator differential equations was developed, a variant of the boundary element method. The main advantage of the new method in comparison with this technique is the reduction of singularities. Main publication: Dobrushkin, V.A. (1983). A general boundary value problem for an abstract differentialoperator equation, Dokl. Akad. Nauk BSSR, 27, 776  779 (in Russian; English summary). The dynamic problems of elasticity for domains with nondifferentiable boundaries pose special difficulties since the standard methods cannot be used reliably for the analysis of wave effects in these geometries. In these domains the effects of wave reflection and diffraction are strongly influenced by the irregular boundary. The solutions of several mixed problems in the dynamic theory of elasticity for the wedgeshaped domains with the coupled boundary conditions (when elastic potentials are not separated) were established. The necessary algorithms for the approximate calculation of these solution have been developed. Main publications: Dobrushkin, V.A. (1988). The boundary value problems in the dynamic theory of elasticity for the wedgeshaped domains. Minsk: Nauka I Technika (in Russian, monograph); Dobrushkin, V.A. (1984). The second boundary value problem of the plane theory of elasticity for a wedge. Dokl. Akad. Nauk SSSR, 1984, 279, No. 11 77 79 (in Russian; English transl. in Soviet Phys. Dokl. 1984, 29, No. 11, 905  907)., 1061  1063. 

Numerical Methods


The appropriate numerical procedure to approximate the value of the continual integral with respect to several measures was developed. Main publication: Dobrushkin, V.A., & Likhoded, N.A. (1982). Approximate calculation of a continual integral with respect to a Cauchy measure with a weight in Hilbert space, 1982, No. 1, 104  106 (in Russian; English summary). 

Approximate evaluation of hypersingular integrals:  
A new method of regularization and approximate calculation of hypersingular integrals and integrodifferential expressions with singularities was proposed. The estimates of quadrature errors were obtained. Main publications: Dobrushkin, V.A. (1992). Regularization in Marchaud form and approximate calculation of a class of integro differential expressions. Izvestiya vuzov. Matematika, 1992, No. 9, .38  41 (in Russian; English transl. in Russian Mathematics. Izvest. VUZ, Matematika, 1992, No. 9, 34  37); Dobrushkin, V.A. (1993). Approximate calculation of a class of integrodifferential expressions that describe the propagation of elastic waves. Prikladn. Mat. i Mech., No. 2, 164 167. (in Russian; English transl. J. Appl. Math. Mechs. 1993, 57, 393  397). 

Mathematical Modelling  
The solution of initialboundary value problem which
simulates halfplane with a semiinfinite crack have been developed.
Main publication: Clifton, R.J., & Dobrushkin,
V.A. Elastic wave propagation in a halfspace containing a buried crack.
Submitted to Wave Motion. 
1999  2000
"Simulation of Coupled Diffusion of Impurity Atoms and Point Defects
in the Vicinities of Interfaces InsulatorSemiconductor and Heterojunctions
SemiconductorSemiconductor" funded by the National Research Council's
Collaboration in Basic Science and Engineering (COBASE). 
Dobrushkin V.A. (2022). Applied Differential Equations. The Primary Course, Chapman & Hall/CRC, 2022, second edition, ISBN13: 9781439851043 Zwillinger, D. and Dobrushkin V.A. (2021). Handbook of Differential Equations, Fourth Edition, Chapman & Hall/CRC, 2021, fourth edition, ISBN13: 9780367252571 Dobrushkin V.A. (2019). Mathematics of Social Choice and Finance, Kendall Hunt Publishing, 2019, second edition, ISBN13: 9781524989590 Dobrushkin V.A. (2017). Applied Differential Equations with Boundary Value Problems, Chapman & Hall/CRC, 2017, ISBN13: 1498733654 Dobrushkin V.A. (2014). Applied Differential Equations. The Primary Course, Chapman & Hall/CRC, 2014, ISBN10:1439851042, ISBN13: 9781439851043 Dobrushkin V.A. (2014). Mathematics of Social Choice and Finance, Kendall Hunt Publishing, 2014, ISBN10: 1465250999, ISBN13: 9781465250995 Dobrushkin V.A. (2009). Methods in Algorithmic Analysis (CRC Computer and Information Science Series), Chapman & Hall/CRC, 2009, ISBN10: 1420068296, ISBN13: 9781420068290 Dobrushkin V.A. (1988). The boundary value problems in the dynamic theory of elasticity for the wedgeshaped domains. Minsk: Nauka i Technika (in Russian). 
47. (with R.A. Beauregard) Multisection of series. The Mathematical Gazette, 100/549, 460  470 (2016). 46. (with R.A. Beauregard) A discrete view of Faa di Bruno. The Rocky Mountain Journal of Mathematics , 46, No. 1, 73  83 (2016). 45. (with R.A. Beauregard) Differential equations vs power series. The Mathematical Gazette, 99/546, 499  503 (2015). 44. (with R.A. Beauregard) Finite sums of the Alcuin Numbers. Mathematics Magazine, 86/4, 280  287 (2013). 43. (with V.A. Tsurko and G.M. Zayats) On convergence of difference schemes for twodimensional secondorder hyperbolic equations with discontinuous coefficients. Matematychni Studii, 31/1, 91  101 (2009). 42. (with M.R. Maxey) An improved boundary element formulation for the motion of spherical bubbles. Differential Equations, 44/9, 1305  1312 (2008). 41. (with F.F. Komarov, O.I. Velichko, and A.M. Mironov) Mechanisms of arsenic clustering in silicon. Physical Review B, 74, July, 0352051  03520510 (2006). 40. (with O. I. Velichko and L. Pakula) A Model of Clustering of Phosphorus Atoms in Silicon. Materials Science and Engineering: B, 123/2, 176  180 (2005). 39. (with I. I. Abramov, V.A. Tsurko, and V.A. Zhuk) Numerical ''Renaissance'' Procedure of Device and Process Parameters in Integrated Circuits. Nonlinear Phenomena in Complex Systems, 78/3, 296  301 (2005) 38. (with A.K. Fedotov and O. I. Velichko) A set of equations for stressmediated evolution of the nonequilibrium dopantdefect system in semiconductor crystals, Journal of Alloys and Compounds, 382, Issue 12, pp. 283287 (2004). 37. (with O. I. Velichko, A. N. Muchynski, V. A. Tsurko, and V. A. Zhuk) Simulation of Coupled Diffusion of Impurity Atoms and Point Defects under Nonequilibrium Conditions in Local Domain. Journal of Computational Physics, 178, 1  14 (2002). 36. (with O. I. Velichko, A. K. Fedotov, V. A. Tsurko) Segregation of Mg Implanted into InAs: Influence of the Internal Elastic Stresses, Diffusion and Defect Data, Part B: Solid State Phenomena, 2002, Vols.8284. pp.569  574. 35. (1994). On solvability of mixed problem in a domain with an angle for wave equation. Sib. J. Diff. Equations, 1994, 3, No. 2, 3  10. 34. (with Nitrebych, Z.N.) (1993). Initial and boundary value problems for hyperbolic partial differential operators with constant coefficient. Sib. J. Diff. Equations, 1993, 2, No. 2, 39  46. 33. (1993). Approximate calculation of a class of integrodifferential expressions that describe the propagation of elastic waves. Prikladn. Mat. i Mech., No. 2, 164 167. (in Russian; English transl. J. Appl. Math. Mechs. 1993, 57, 393  397). 32. (with Kolesnikov, A.N., Podkopaev, P.A., & Shestokov, V.N.) (1993). Algorithm for calculation of strainstress state of elastic semiplane. Vesty Akad Nauk Belarus, ser. fiz.mat. nauk, 1993, No. 2, 219. 31. (1992). Regularization in Marchaud form and approximate calculation of a class of integro differential expressions. Izvestiya vuzov. Matematika, 1992, 36, No. 9, 38  41 (in Russian; English transl. in Russian Mathematics. Izvest. VUZ, Matematika, 1992, No. 9, 34  37). 30. (with Djum, T.R.) (1992). On the solution of the Cauchy problem for the Lame operator and its regularization. Differ. Uravn., 1992, 28, No. 10, 1830  1833.(in Russian; English summary). 29. (1990). Regularization and approximate calculation of the Marchaud's derivative of a twodimensional integral with sliding singularities. In: Some applications of functional analysis to the problems of mathematical physics. Novosibirsk: Mathematical institute of Siberian branch of the Academy of Science of the USSR, 1990, 81  91 (in Russian). 28. (1989). Approximate calculation of the Marchaud's derivative of a twodimensional integral with singularities. Dokl. Akad. Nauk BSSR, 1989, 33, 101  103 (in Russian; English summary). 27. (with Podkopaev, P.A.) (1988). On the solution of the first boundary value problem of elastodynamics for the plane with cracks. Minsk, 1988. 38 pp. (Preprint /Mathematical Institute, Byelorussian Academy of Science, No. 9 (319)) (in Russian). 26. (with Podkopaev,P.A.) (1986). Mathematical investigation of the first boundary value problem of elasticity for the plane with two semiinfinite cracks. Minsk, 1986. 28 pp. (Preprint /Mathematical Institute, Byelorussian Academy of Science; No. 20 (256)) (in Russian). 25. (with Podkopaev, P.A.) (1986). Mathematical investigation of the first boundary value problem of elasticity for the plane with semiinfinite crack. Minsk, 1986. 32 pp. (Preprint /Mathematical Institute, Byelorussian Academy of Science; No. 19 (255)) (in Russian). 24. (1986). Solution of the second boundary value problem of elasticity theory for a semiband. Differ. Uravn., 1986, 22, No. 6, 987 993 (in Russian; English transl. in Differential Equations, 1986, 22, 697  702). 23. (1985). Analytical solution of a static boundary value problem of the plane theory of elasticity. Differ. Uravn., 1985, 21, No. 4, 717  720 (in Russian; English summary). 22. (1985). Solution of the second boundary value problem of the theory of elasticity elasto for a wedge. Izvest. Akad. Nauk BSSR, ser. fiz.mat. nauk, 1985. No. 4, 8  13 (in Russian; English summary). 21. (1984). About certain problems of ordering of noncommutative operators and continual integration. Minsk, 1984, 18 pp. (Preprint /Mathematical Institute, Byelorussian Academy of Science; No. 14 (199)) (in Russian; English summary). 20. (1984). The second boundary value problem of the plane theory of elasticity for a wedge. Dokl. Akad. Nauk SSSR, 1984, 279, No. 11 77 79 (in Russian; English transl. in Soviet Phys. Dokl. 1984, 29, No. 11, 905  907). 19. (1984). Solution of the first boundary value problem of the theory of elasticity for a quadrant. Dokl. Akad. Nauk BSSR, 1984, 28, No. 2, 115  118 (in Russian; English summary). 18. (1983). A general boundary value problem for an abstract operatordifferential equation. Dokl. Akad. Nauk BSSR, 1983, 27, No. 9, 776  779 (in Russian; English summary). 17. (with Podkopaev, P.A.) (1983). Representation of the solutions of boundary value problems for the heat equation in the form of a continual integral with respect to. a Wiener measure. Izvest. Akad. Nauk BSSR, ser. fiz.mat. nauk, 1983, No. 6, 9  14 (in Russian; English summary) 16. (with Lihoded, N.A.) (1982). On approximate evaluation of continual integrals with respect to measures corresponding to a Markov process of telegraph type. Dokl. Akad. Nauk BSSR, 1982, 26, No. 11. 965  968 (in Russian; English summary). 15. (with Lihoded, N.A.) (1982). On approximate calculation of continual integral with respect to a Cauchy's measure with weight in the Hilbert space. Izvest. Akad. Nauk BSSR, ser. fiz.mat. nauk, 1982, No. 1, 104  106 (in Russian; English summary). 14. (1981). Evaluation of continual integrals with respect to Cauchy's, Abel's and Gauss's measures in the product of Hilbert spaces. Minsk, 1981, 40 pp. (Preprint /Mathematical Institute, Byelorussian Academy of Science; No. 2 (103)) (in Russian). 13. (1981). The KolmogorovKhinchin criterion for certain measures in the space W. Izvest. Akad. Nauk BSSR, ser. fiz.mat. nauk, 1981, No. 6, 120  123 (in Russian; English summary). 12. (1981). Generalized summation of continual integrals. Izvest. Akad. Nauk BSSR, ser. fiz.mat. nauk, 1981, No. 5. 5  10 (in Russian; English summary 11. (1980). Investigation of the problem on simultaneous thermal and mechanical shocks onto a composite finite rod. Izvest. Akad. Nauk BSSR, ser. fiz.mat. nauk, 1980, No. 4, 20  27 (in Russian; English summary). 10. (1979). Cezaro's summation of certain series and integrals.  Minsk, 1979. 16 pp. (Preprint /Mathematical Institute, Byelorussian Academy of Science; No. 1(57)) (in Russian). 9. (with Gaiduk, S.I.). (1979). Solution of a problem in the theory of thermoelasticity related to mechanical and thermal shocks. Differ. Uravn., 1979, 15, No. 9, 1632  1645 (in Russian; English transl. in Differential equations, 1979, 15, No. 9, 1165  1174). 8. (1978). Investigation of several initial boundary value problems about the impact onto the semiinfinite beams. Minsk, 1978, 29pp. (Preprint /Mathematical Institute, Byelorussian Academy of Science; No. 6 (38))(in Russian). 7. (1978). A dynamic problem of shock theory for an elastic plate. Dokl. Akad. Nauk BSSR, 1978, 22, No. 3, 197  199 (in Russian; English summary ). 6. (1978). The solution of a problem of a shock on elastic semiinfinite plate. Izvest. Akad. Nauk BSSR, ser. fiz.mat. nauk, 1978, No. 1, 134 (in Russian; English summary). 5. (1977). Solution of a problem of a longitudinal shock along an inhomogeneous viscoelastically relaxing rod. Differ. Uravn., 1977, 13, No. 9, 1658  1666 (in Russian; English transl. in Differential Equations, 1977, 13, No. 9, 1155  1160). 4. (1977). The uniqueness of the generalized solution of a certain problem in shock theory. Differ. Uravn., 1977, 13, No. 8, 15211523. English transl. in Differential Equations, 13, 1061  1063. 3. (1976). A problem in the theory of longitudinal vibrations of an elasticviscousrelaxing rod. Izvest. Akad. Nauk BSSR, ser. fiz.mat. nauk, 1976, No. 5, 53  60 (in Russian; English summary). 2. (with Gaiduk S.I.).
(1975). Solution of a problem of longitudinal shock along a viscoelastically
relaxing rod. Izvest. Akad. Nauk BSSR, ser. fiz.mat. nauk,
1975. No. 6, 30  41 (in Russian; English summary).
