Yuri A. Antipov

Department of Mathematics
388 Lockett Hall
Louisiana State University
Baton Rouge, LA  70803

Email: antipov@math.lsu.edu
Phone: (225) 578-1567
Fax: (225) 578-4276

My main research interests are mathematical modeling in dynamic fracture mechanics, penetration mechanics, aeroelasticity, fluid dynamics (supercavitating flow), and scattering of sound and electromagnetic waves. I am particularly interested in the development of exact and approximate methods for the vector Riemann-Hilbert boundary-value problem, difference equations with variable coefficients, singular integral equations, and applications of the theory of automorphic functions and Riemann surfaces to model problems in applied mechanics and nonlinear physics.

Complex Variables and Elliptic Equations

Education

Ph.D. (Doctor in Sciences), Solid Mechanics, Department of Mechanics and Mathematics, Moscow State University, 1993

Ph.D. (Candidate in Sciences), Differential Equations and Mathematical Physics, Department of Mechanics and Mathematics, Odessa State University, 1983

Diploma, Applied Mathematics, Department of Mechanics and Mathematics, Odessa State University, 1979

Work Experience

2002-present: Professor (since 2004) and Associate Professor (02-04) Department of Mathematics, Louisiana State University, Louisiana

1997-2002: Lecturer (99-02) and Research Officer (97-98), Department of Mathematical Sciences, The University of Bath, England

1996-1997: Fellow of the Alexander von Humboldt Foundation, Institute of Mathematics A, The University of Stuttgart, Germany

1995-1996: Chair, Department of Theoretical Mechanics, Odessa Institute of Civil Engineering, Odessa.

1982-1995: Professor (94-95), Docent (84-94), and Assistant (82-84), Department of Mechanics and Mathematics, Odessa State University.

    Publications

  1. Y.A. Antipov, Plane and axisymmetric problems of an interfacial crack in a power-law graded material, Proc. Roy. Soc. (2023) 479, no. 2279, Paper No. 20230630.

  2. Y.A.Antipov, Scattering by a perforated sandwich panel: method of Riemann surfaces, Quart. J. Mech. Appl. Math. (2023) 76, 243-275.

  3. Y.A.Antipov, S.M. Mkhitaryan, Hertzian and adhesive plane models of contact of two inhomogeneous elastic bodies, European J. Appl. Math. (2023) 34, 667-700.

  4. Y.A. Antipov, A free boundary problem of elasticity in an angle and a vector Riemann-Hilbert problem on a torus, Physica D (2023) 444, Paper No. 133601.

  5. Y.A. Antipov and A.Y. Zemlyanova, Riemann-Hilbert problem on a torus and a vortex patch in a wedge, Complex Variables and Elliptic Equations (2022), 67 (6), 2878-2906.

  6. Y.A.Antipov, S.M. Mkhitaryan, Axisymmetric contact of two different power-loaw gradede elastic bodies and an integral equation with two Weber-Schafheitlin kernels, Quart. J. Mech. Appl. Math. (2022) 75, 393-420.

  7. Y.A. Antipov, Riemann-Hilbert problem on a hyperelliptic surface and uniformly stressed inclusions embedded into a half-plane subjected to antiplane strain, Proc. Roy. Soc. A. (2021), 20210350.

  8. Y.A.Antipov, S.M. Mkhitaryan, Integral and integro-differential equations with an exponential kernel and applications, Quart. J. Mech. Appl. Math. (2021) 74, 297-322.

  9. Y.A. Antipov Coupled flight dynamics and thermoelasticity model of maneuvering aircraft, AIAA J. (2020), 58:10, 4563-4579.

  10. Y.A. Antipov, S.M. Mkhitaryan, Annular and circular rigid inclusions planted into a penny-shaped crack and factorization of triangular matrices, Proc. Roy. Soc. A. (2020), 476: 2238.

  11. Y.A.Antipov, Method of Riemann surfaces for an inverse antiplane problem in an n-connected domain, Complex Variables and Elliptic Equations (2020), 65 (3), 455-480.

  12. Y.A. Antipov, S.M. Mkhitaryan, Correspondence principle in plane and axisymmetric mixed boundary-value problems of elasticity, Quart. Appl. Math. (2020), 78, 333-362.

  13. Y.A.Antipov, Rapid transient motion of a thin rigid body in an elastic medium, SIAM J. Appl. Math. (2019), 79, 2080-2106.

  14. Y.A. Antipov, Exact solution to the problem of acoustic wave propagation in a semi-infinite waveguide with flexible walls, Wave Motion (2019) 91, 102386.

  15. Y.A.Antipov, Method of automorphic functions for an inverse problem of antiplane elasticity, Quart. J. Mech. Appl. Math. (2019) 72, 213-234.

  16. Y.A. Antipov, S.M. Mkhitaryan, Integral relations associated with the semi-infinite Hilbert transform and applications to singular integral equations, Quart. Appl. Math. (2018) 76, 739-766.

  17. Y.A.Antipov, Subsonic frictional cavitating penetration of a thin rigid body into an elastic medium, Quart. J. Mech. Appl. Math. (2018) 71, 221-243.

  18. Y.A. Antipov, Slit maps in the study of equal-strength cavities in n-connected elastic planar domains, SIAM J. Appl. Math. (2018) 78, 320-342.

  19. Y.A. Antipov, B.T. Dickinson, Dynamic problem of coupled thermoelasticity for a thin composite structure, Mathematics and Mechanics of Solids, (2018) 23, 1274-1290.

  20. Y.A. Antipov, S.M. Mkhitaryan, A crack induced by a thin rigid inclusion partly debonded from the matrix, Quart. J. Mech. Appl. Math. (2017) 70, 153-185.

  21. Y.A. Antipov, A.V. Smirnov, Fundamental solution and the weight functions of the transient problem on a semi-infinite crack propagating in a half-plane, Z. Angew. Math. Mech. (ZAMM) (2016) 96, 1156-1174.

  22. Y.A. Antipov, Singular integral equations with two fixed singularities and applications to fracture composites, Quart. J. Mech. Appl. Math. (2015) 68, 461-501.

  23. Y.A. Antipov, Vector Riemann-Hilbert problem with almost periodic and meromorphic coefficients and applications, Proc. R. Soc. A. (2015) 471, 20150262.

  24. Y.A. Antipov, The Baker-Akhiezer function and factorization of the Chebotarev-Khrapkov matrix, Letters in Mathematical Physics (2014), 104, 1365-1384.

  25. Y.A. Antipov, Nonlinear bending models for beams and plates, Proc. R. Soc. A. (2014) 470, 20140064.

  26. Y.A. Antipov, Diffraction of an obliquely incident electromagnetic wave by an impedance right-angled concave wedge, Quart. J. Mech. Appl. Math. (2014) 67, 1-42.

  27. Y.A. Antipov and A.V. Smirnov, Subsonic propagation of a crack parallel to the boundary of a half-plane, Mathematics and Mechanics of Solids, (2013) 18 (2), 153-167.

  28. Y.A. Antipov, Weight functions of a crack in a two-dimensional micropolar solid, Quart. J. Mech. Appl. Math. (2012) 65, 239-271.

  29. Y.A. Antipov, R. Estrada, and B. Rubin, Method of analytical continuation for the inverse spherical mean transform in constant curvature spaces, Journal d'Analyse Mathematique, 2012, 118, 623-656.

  30. Y.A. Antipov and B. Rubin, A generalization of the Mader-Helgason inversion formulas for the Radon transforms, Transactions of the AMS, (2012) 364, 6479-6493.

  31. A.Y. Zemlyanova and Y.A. Antipov, Single-spiral-vortex model for a cavitating elastic curvilinear foil, SIAM J. Appl. Math. (2012) 72, 280-298.

  32. Y.A. Antipov, A genus-3 Riemann-Hilbert problem and diffraction of a wave by orthogonal resistive half-planes, Computational Methods and Function Theory (2011) 11, 439-462.

  33. Y.A. Antipov and P. Schiavone, Integro-differential equation of a finite crack in a strip with surface effects, Quart. J. Mech. Appl. Math. (2011) 64, 87-106. Corrections in Abstract and Conclusions.

  34. Y.A. Antipov, A symmetric Riemann-Hilbert problem for order-4 vectors in diffraction theory, Quart. J. Mech. Appl. Math. (2010) 63, 349-374.

  35. Y.A. Antipov and V.V. Silvestrov, Hilbert problem for a multiply connected circular domain and the analysis of the Hall effect in a plate, Quart. Appl. Math. (2010) 68, 563-590.

  36. Y.A. Antipov, Subsonic semi-infinite crack with a finite friction zone in a bimaterial, J. Mech. Phys. Solids (2009) 57, 1934-1957.

  37. Y.A. Antipov and A.Y. Zemlyanova, Motion of a yawed supercavitating wedge beneath a free surface, SIAM J. Appl. Math. (2009) 70, 923-948.

  38. Y.A. Antipov and A.Y. Zemlyanova, Single- and double-spiral vortex models for a supercavitating nonsymmetric wedge in a jet, Proc. Roy. Soc. Lond. A (2009) 465, 3817-3837.

  39. Y.A. Antipov and V.V. Silvestrov, Circular map for supercavitating flow in a multiply connected domain, Quart. J. Mech. Appl. Math. (2009) 62, 167-200.

  40. Y.A. Antipov and V.V. Silvestrov, Double cavity flow past a wedge, Proc. Roy. Soc. Lond. A, (2008) 464, 3021-3038.

  41. Y.A. Antipov and V.V. Silvestrov, Diffraction of a plane wave by a right-angled penetrable wedge, Radio Science (2007) 42, RS4006, 1-15.

  42. Y.A. Antipov and D.G. Crowdy, Riemann-Hilbert problem for automorphic functions and the Schottky-Klein function, Complex Analysis and Operator Theory (2007) 1, 317-334.

  43. Y.A. Antipov and J.R.Willis, Propagation of a Mode-II crack in a viscoelastic medium with different bulk and shear relaxation, Journal of Engineering Mathematics (2007) 359-371.

  44. Y.A. Antipov and V.V. Silvestrov, Method of Riemann surfaces in the study of supercavitating flow around two hydrofoils in a channel, Physica D (2007) 235, 72-81.

  45. Y.A. Antipov and V.V. Silvestrov, Method of integral equations for systems of difference equations , IMA J. Appl. Math. (2007) 72, 681-705.

  46. Y.A. Antipov and V.V. Silvestrov, Method of automorphic functions in the study of flow around a stack of porous cylinders, Quart. J. Mech. Appl. Math., (2007) 60, 337-366.

  47. Y.A. Antipov and V.V. Silvestrov, Electromagnetic scattering from an anisotropic half-plane at oblique incidence: the exact solution, Quart. J. Mech. Appl. Math., (2006) 59, 211-251.

  48. Y.A. Antipov and A.S. Fokas, The modified Helmholtz equation in a semi-strip, Math. Proc. Cambridge Phil. Soc., (2005) 138, 339-365.

  49. J.P. Bercial-Velez, Y.A. Antipov and A.B. Movchan, High order asymptotics and perturbation problems for 3D interfacial cracks, J. Mech. Phys. Solids (2005) 53, 1128-1162.

  50. Y.A. Antipov and V.V. Silvestrov, Second-order functional-difference equations. I.: Method of the Riemann-Hilbert problem on Riemann surfaces, Quart. J. Mech. Appl. Math., (2004) 57(2), 245-265.

  51. Y.A. Antipov and V.V. Silvestrov, Second-order functional-difference equations. II.: Scattering from a right-angled conductive wedge for E-polarization, Quart. J. Mech. Appl. Math., (2004) 57(2), 267-313.

  52. Y.A. Antipov, O. Obrezanova, and J.R. Willis, A fracture criterion of ``Barenblatt'' type for a transonic shear crack, Mathematics and Mechanics of Solids, (2004) 9, 271-283.

  53. Y.A. Antipov and V.V. Silvestrov, Vector functional-difference equation in electromagnetic scattering, IMA J. Appl. Math., (2004) 69, 27-69.

  54. Y.A. Antipov and P. Schiavone, On the uniformity of stresses inside an inhomogeneity of arbitrary shape, IMA J. Appl. Math., (2003) 68, 299-311.

  55. Y.A. Antipov, T.-J. Chuang and H. Gao, On the integro-differential equation associated with diffusive crack growth theory, Quart. J. Mech. Appl. Math., (2003) 56(2), 289-310.

  56. Y.A. Antipov and V.V. Silvestrov, Method of hyperelliptic surfaces for vector functional-difference equations, IUTAM Symposium on Asymptotics, Singularities and Homogenisation in Problems of Mechanics, Editor: A.B. Movchan, 33-42, Kluwer Acad. Publ., Dordrecht et al (2003).

  57. Y.A. Antipov and J.R. Willis, Transient loading of a rapidly-advancing Mode-II crack in a viscoelastic medium, Mechanics of Materials, (2003) 35, 415-431.

  58. Y.A. Antipov and V.V. Silvestrov, Factorization on a Riemann surface in scattering theory, Quart. J. Mech. Appl. Math., (2002) 55, 607-654.

  59. Y.A. Antipov and H. Gao, Atomic diffusion from a material surface into a grain boundary, Proc. Roy. Soc. Lond. A (2002), 458, 1673-1694.

  60. Y.A. Antipov, Diffraction of a plane wave by a circular cone with an impedance boundary condition, SIAM J. Appl. Math. (2002), 62, 1122-1152.

  61. Y.A. Antipov, Diffraction coefficients for a circular impedance cone, IUTAM Symposium on Diffraction and Scattering in Fluid Mechanics and Elasticity, Editors: I.D.Abrahams et al, 151-158, Kluwer Acad. Publ., Dordrecht et al (2002).

  62. Y.A. Antipov, An integro-differential equation of atomic diffusion, Integral Methods in Science and Engineering, Editors: P. Schiavone et al, 39-44, Birkhaeuser, Boston at al (2002).

  63. Y.A. Antipov, Solution by quadratures of the problem of a cylindrical crack by the method of matrix factorization, IMA J. Appl. Math., (2001), 66, 591-619.

  64. Y.A. Antipov, O. Avila-Pozos, S.T. Kolaczkowski and A.B. Movchan, Mathematical model of delamination cracks on imperfect interfaces, Int. J. Solids Structures, (2001), 38, 6665-6697.

  65. Y.A. Antipov, A.B. Movchan and S.T. Kolaczkowski, Models of fracture of cellular monolith structures, Int. J. Solids Structures, (2001), 38, 1659-1668.

  66. Y.A. Antipov and H. Gao, Exact solution of integro-differential equations of diffusion along a grain boundary, Quart. J. Mech. Appl. Math., (2000), 53, 645-674.

  67. C.G. Poulton, A.B. Movchan, R.C. McPhedran, N.A. Nicorovichi and Y.A. Antipov, Eigenvalue problems for doubly periodic elastic structures and phononic band gaps, Proc. Roy. Soc. Lond. A, (2000), 456,2543-2559.

  68. Y.A. Antipov and D. Bardzokas, An analytical method of solution of mixed problems of the theory of elasticity, Acta Mechanica, (2000), 141, No 1-2, 99-116.

  69. Y.A. Antipov, A.B. Movchan and N.V. Movchan, Frictional contact of a fibre and an elastic solid, J. Mech. Phys. Solids, (2000), 48, 1413-1439.

  70. Y.A. Antipov, Galin's problem for a periodic system of stamps with friction and adhesion, Int. J. Solids Structures, (2000), 37, 2093-2125.

  71. Y.A. Antipov, S.T. Kolaczkowski, A.B. Movchan and A. Spence, Asymptotic analysis for cracks in a catalytic monolith combustor, Int. J. Solids Structures, (2000), 37, 1899-1930.

  72. Y.A. Antipov, An exact solution of the 3-D-problem on an interface semi-infinite plane crack, J. Mech. Phys. Solids (1999), 47, 1051-1093.

  73. Y.A. Antipov, D. Bardzokas and G.E. Exadactylos, Interface edge crack in a bimaterial elastic half-plane, Int. J. Fracture, (1998), 88, 281-304.

  74. Y.A. Antipov, D. Bardzokas and G.E. Exadactylos, Partially stiffened elastic half-plane with edge crack, Int. J. Fracture, (1997), 85, 241-263.

  75. Y.A. Antipov, A delaminated inclusion in the case of adhesion and slippage, J. Appl. Math. Mech. (PMM), (1996), 60, 665-675.

  76. Y.A. Antipov, An interface crack between elastic materials when there is dry friction, J. Appl. Math. Mech. (PMM), (1995), 59, 273-287.

  77. Y.A. Antipov and N.Kh. Arutyunyan, On the interaction of a semi-infinite stringer with a half-plane and a strip under slip-stick conditions, Mechanics of Solids (MTT), (1993), 28, No 4, 171-178.

  78. Y.A. Antipov, An efficient solution of Prandtl-type integro-differential equations in a section and its application to contact problems for a strip, J. Appl. Math. Mech. (PMM), (1993), 57, 547-556.

  79. Y.A. Antipov and N.Kh. Arutyunyan, A contact problem with friction and adhesion for an elastic layer with stiffeners, J. Appl. Math. Mech. (PMM), (1993), 57, 159-170.

  80. Y.A. Antipov, Deformation potential energy increment for a crack crossing a boundary line between media, Mechanics of Solids (MTT), (1993), 28, No 1, 129-139.

  81. Y.A. Antipov and N.Kh. Arutyunyan, Contact problems of elasticity theory for wedge-shaped regions under conditions of friction and adhesion, J. Appl. Math. Mech. (PMM), (1992), 56, 603-615.

  82. Y.A. Antipov and N.Kh. Arutyunyan, On principle of correspondence under torsion of inhomogeneous axisymmetric bodies, Dokl. Armenian AN, (1992), 93, No 1, 23-27.

  83. Y.A. Antipov and N.Kh. Arutyunyan, Contact problems of the theory of elasticity with friction and adhesion, J. Appl. Math. Mech. (PMM), (1991), 55, 887-901.

  84. Y.A. Antipov and N.G. Moiseyev, Exact solution of the plane problem for a composite plane with a cut across the boundary between two media, J. Appl. Math. Mech. (PMM), (1991), 55, 531-539.

  85. Y.A. Antipov and N.Kh. Arutyunyan, Torsion of a composite sphere with an annular or penny-shaped crack, Mechanics of Solids (MTT), (1991), 26, No 4, 83-95.

  86. Y.A. Antipov, Analytic solution of a two-dimensional problem for a half-plane with a crack that is close to the boundary, Studies in elasticity and plasticity, (1990), No. 16, 14-23, 204, Leningrad. Univ., Leningrad.

  87. Y.A. Antipov and N.Kh. Arutyunyan, Torsion of an elastic ball with a penny-shaped crack, Mechanics of Solids (MTT), (1990), 25, No 3, 32-40.

  88. Y.A. Antipov, Analytic solution of mixed problems of mathematical physics with a change of boundary conditions over a ring, Mechanics of Solids (MTT), (1989), 24, No 3, 49-56.

  89. Y.A. Antipov and G.Ya. Popov, The plane state of stress of an elastic plane with two intersecting slits, J. Appl. Math. Mech. (PMM), (1988), 52, 479-488.

  90. Y.A. Antipov, G.Ya. Popov and S.I. Yatsko, Solution of the problem of stress concentration around intersecting defects by using the Riemann problem with an infinite index, J. Appl. Math. Mech. (PMM), (1987), 51, 357-365.

  91. Y.A. Antipov, Exact solution of the problem on pressing of a flat annular punch into the half-space, Dokl. Ukrainian AN, (1987), A, 7, 29-33.

  92. Y.A. Antipov, A.F. Daszczenko and A.P. Popova, Mixed boundary-value problems on stress concentration in a half-space near a crack and a stiffener, In Solid Mechanics, 68-73, Erevan (1985).

  93. Y.A. Antipov, Some mixed boundary-value problems of torsion on stress concentration in bars, In Dynamic Systems, 64-72, Kiev (1983).

  94. Y.A. Antipov, A.F. Daszczenko and G.Ya. Popov, On some torsion problems of bars with cracks and inclusions, Izv. Armenian AN Mechanics (1982), 35, No 2, 27-42.

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