Yuri A. Antipov
Department of Mathematics
388 Lockett Hall
Louisiana State University
Baton Rouge, LA 70803
Email: antipov@math.lsu.edu
Phone: (225) 5781567
Fax: (225) 5784276
My main research interests are mathematical modeling in dynamic
fracture mechanics, penetration mechanics,
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 RiemannHilbert boundaryvalue 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
2002present: Professor (since 2004) and
Associate Professor (0204)
Department of Mathematics,
Louisiana State University, Louisiana
19972002: Lecturer (9902) and Research Officer (9798), Department of
Mathematical Sciences,
The University of Bath, England
19961997: Fellow of the
Alexander von Humboldt Foundation,
Institute of Mathematics A,
The University of Stuttgart, Germany
19951996: Chair, Department of Theoretical Mechanics, Odessa Institute
of Civil
Engineering, Odessa.
19821995: Professor (9495), Docent (8494), and
Assistant (8284),
Department of Mechanics and Mathematics, Odessa State University.
Publications

Y.A. Antipov, S.M. Mkhitaryan, Integral relations associated with the
semiinfinite Hilbert transform and applications to singular integral equations,
Quart. Appl. Math.
(2018) 76, 739766.

Y.A.Antipov,
Subsonic frictional cavitating penetration of a thin rigid body into an elastic medium, Quart. J. Mech. Appl. Math.
(2018) 71, 221243.

Y.A. Antipov,
Slit maps in the study of equalstrength cavities in nconnected elastic planar domains,
SIAM J. Appl. Math. (2018) 78, 320342.

Y.A. Antipov, B.T. Dickinson,
Dynamic problem of coupled thermoelasticity for a thin composite structure,
Mathematics and Mechanics of
Solids, (2018) 23, 12741290.

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, 153185.

Y.A. Antipov, A.V. Smirnov,
Fundamental solution and the weight functions of the transient problem on a semiinfinite crack
propagating in a halfplane, Z. Angew. Math. Mech. (ZAMM)
(2016) 96, 11561174.

Y.A. Antipov,
Singular integral equations with two fixed singularities and applications to fracture composites,
Quart. J. Mech. Appl. Math.
(2015) 68, 461501.

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

Y.A. Antipov,
The BakerAkhiezer function and factorization of the ChebotarevKhrapkov matrix,
Letters in Mathematical Physics
(2014), 104, 13651384.

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

Y.A. Antipov,
Diffraction of an obliquely incident electromagnetic wave by an impedance rightangled concave wedge,
Quart. J. Mech. Appl. Math.
(2014) 67, 142.

Y.A. Antipov and A.V. Smirnov,
Subsonic propagation of a crack parallel to the boundary of a halfplane,
Mathematics and Mechanics of
Solids, (2013) 18 (2), 153167.

Y.A. Antipov, Weight functions of a crack in a twodimensional micropolar solid,
Quart. J. Mech. Appl. Math.
(2012) 65, 239271.

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, 623656.

Y.A. Antipov and
B. Rubin,
A generalization of the
MaderHelgason inversion formulas for
the Radon transforms,
Transactions of the AMS, (2012) 364, 64796493.

A.Y. Zemlyanova and Y.A. Antipov,
Singlespiralvortex model for a cavitating elastic curvilinear foil,
SIAM J. Appl. Math. (2012) 72, 280298.

Y.A. Antipov,
A genus3 RiemannHilbert problem and diffraction of a wave by
orthogonal resistive halfplanes,
Computational Methods and Function Theory (2011) 11, 439462.

Y.A. Antipov and
P. Schiavone,
Integrodifferential equation of a finite crack in a strip with surface
effects, Quart. J. Mech. Appl. Math.
(2011) 64, 87106.
Corrections in Abstract and Conclusions.

Y.A. Antipov,
A symmetric RiemannHilbert problem for order4 vectors
in diffraction theory,
Quart. J. Mech. Appl. Math.
(2010) 63, 349374.

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, 563590.

Y.A. Antipov,
Subsonic semiinfinite crack with a finite friction zone
in a bimaterial,
J. Mech. Phys. Solids (2009) 57, 19341957.

Y.A. Antipov and A.Y. Zemlyanova,
Motion of a yawed supercavitating
wedge beneath a free surface,
SIAM J. Appl. Math.
(2009) 70, 923948.

Y.A. Antipov and A.Y. Zemlyanova,
Single and doublespiral vortex models
for a supercavitating nonsymmetric wedge in a jet,
Proc. Roy. Soc. Lond. A (2009) 465, 38173837.

Y.A. Antipov and V.V. Silvestrov,
Circular map for supercavitating
flow in a multiply connected domain,
Quart. J. Mech. Appl. Math.
(2009) 62, 167200.

Y.A. Antipov and V.V. Silvestrov,
Double cavity flow past a wedge,
Proc. Roy. Soc. Lond. A, (2008) 464, 30213038.

Y.A. Antipov and V.V. Silvestrov,
Diffraction of a plane wave by a rightangled penetrable wedge,
Radio Science (2007) 42, RS4006, 115.

Y.A. Antipov and D.G. Crowdy,
RiemannHilbert problem for automorphic functions and the SchottkyKlein
function,
Complex Analysis and Operator Theory (2007) 1, 317334.

Y.A. Antipov
and J.R.Willis,
Propagation of a ModeII crack in a viscoelastic medium with different
bulk and shear relaxation,
Journal of Engineering Mathematics (2007) 359371.

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, 7281.

Y.A. Antipov and V.V. Silvestrov,
Method of integral equations for systems of difference equations
,
IMA J. Appl. Math. (2007) 72, 681705.

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, 337366.

Y.A. Antipov and V.V. Silvestrov,
Electromagnetic scattering from an anisotropic halfplane at oblique
incidence: the exact solution,
Quart. J. Mech. Appl. Math., (2006) 59, 211251.

Y.A. Antipov and A.S. Fokas,
The modified Helmholtz equation
in a semistrip,
Math. Proc. Cambridge Phil. Soc.,
(2005) 138, 339365.
 J.P. BercialVelez,
Y.A. Antipov and A.B. Movchan,
High order asymptotics and perturbation
problems for 3D interfacial cracks,
J. Mech. Phys. Solids (2005) 53, 11281162.
 Y.A. Antipov and V.V. Silvestrov,
Secondorder functionaldifference
equations. I.: Method of the RiemannHilbert problem on Riemann surfaces,
Quart. J. Mech. Appl. Math., (2004) 57(2), 245265.
 Y.A. Antipov and V.V. Silvestrov,
Secondorder functionaldifference
equations. II.: Scattering from a rightangled conductive wedge for
Epolarization, Quart. J. Mech. Appl. Math.,
(2004) 57(2), 267313.

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, 271283.

Y.A. Antipov and V.V. Silvestrov,
Vector functionaldifference equation in electromagnetic scattering,
IMA J. Appl. Math., (2004) 69, 2769.

Y.A. Antipov and P. Schiavone,
On the uniformity of stresses inside an inhomogeneity
of arbitrary shape, IMA J. Appl. Math., (2003) 68, 299311.

Y.A. Antipov, T.J. Chuang
and H. Gao,
On the integrodifferential
equation associated with diffusive crack growth theory,
Quart. J. Mech. Appl. Math., (2003) 56(2), 289310.

Y.A. Antipov and V.V. Silvestrov,
Method of hyperelliptic surfaces for vector functionaldifference equations,
IUTAM Symposium on Asymptotics, Singularities and Homogenisation in Problems of Mechanics, Editor: A.B. Movchan, 3342, Kluwer Acad. Publ.,
Dordrecht et al (2003).

Y.A. Antipov and J.R. Willis,
Transient loading of a rapidlyadvancing ModeII
crack in a viscoelastic medium,
Mechanics of Materials, (2003) 35, 415431.
 Y.A. Antipov and V.V. Silvestrov,
Factorization
on a Riemann surface
in scattering theory, Quart. J. Mech. Appl. Math.,
(2002) 55, 607654.
 Y.A. Antipov and H. Gao,
Atomic diffusion
from a material surface into a grain boundary,
Proc. Roy. Soc. Lond. A
(2002), 458, 16731694.
 Y.A. Antipov,
Diffraction of a plane wave by a circular cone
with an impedance boundary condition,
SIAM J. Appl. Math.
(2002), 62, 11221152.

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, 151158, Kluwer Acad. Publ.,
Dordrecht et al (2002).

Y.A. Antipov, An integrodifferential equation of atomic diffusion,
Integral Methods in Science and Engineering, Editors:
P. Schiavone et al, 3944, Birkhaeuser, Boston at al (2002).
 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, 591619.

Y.A. Antipov, O. AvilaPozos,
S.T. Kolaczkowski and A.B. Movchan,
Mathematical model of delamination cracks on imperfect interfaces,
Int. J. Solids Structures, (2001), 38, 66656697.

Y.A. Antipov, A.B. Movchan and S.T. Kolaczkowski,
Models of fracture of cellular monolith structures,
Int. J. Solids Structures, (2001), 38, 16591668.

Y.A. Antipov and H. Gao,
Exact solution of integrodifferential equations of diffusion
along a grain boundary,
Quart. J. Mech. Appl. Math., (2000), 53,
645674.
 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), 456,25432559.
 Y.A. Antipov and D. Bardzokas, An analytical method of
solution of mixed problems
of the theory of elasticity, Acta Mechanica, (2000), 141,
No 12, 99116.
 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, 14131439.
 Y.A. Antipov, Galin's problem for a periodic
system of stamps with friction
and adhesion, Int. J. Solids Structures, (2000), 37, 20932125.
 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, 18991930.
 Y.A. Antipov,
An exact solution of the 3Dproblem on an interface semiinfinite
plane crack, J. Mech. Phys. Solids (1999), 47, 10511093.
 Y.A. Antipov, D. Bardzokas and G.E. Exadactylos,
Interface edge crack in a bimaterial elastic halfplane,
Int. J. Fracture, (1998), 88, 281304.
 Y.A. Antipov, D. Bardzokas and G.E. Exadactylos,
Partially stiffened elastic
halfplane with edge crack, Int. J. Fracture, (1997), 85, 241263.
 Y.A. Antipov, A delaminated inclusion in the case of adhesion
and slippage, J. Appl. Math. Mech. (PMM), (1996), 60, 665675.

Y.A. Antipov, An interface crack between elastic materials when
there is dry friction, J. Appl. Math. Mech. (PMM), (1995), 59, 273287.
 Y.A. Antipov and N.Kh. Arutyunyan, On the interaction of a
semiinfinite stringer with a halfplane and a strip under slipstick
conditions, Mechanics of Solids (MTT), (1993), 28, No 4, 171178.

Y.A. Antipov, An efficient solution of Prandtltype
integrodifferential equations in a section and its application to contact
problems for a strip, J. Appl. Math. Mech. (PMM), (1993), 57, 547556.
 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, 159170.
 Y.A. Antipov, Deformation potential energy increment for a crack
crossing a boundary line between media, Mechanics of Solids (MTT),
(1993),
28, No 1, 129139.
 Y.A. Antipov and N.Kh. Arutyunyan, Contact problems of elasticity
theory for wedgeshaped regions under conditions of friction and adhesion,
J. Appl. Math. Mech. (PMM), (1992), 56, 603615.
 Y.A. Antipov and N.Kh. Arutyunyan, On principle of correspondence
under torsion of inhomogeneous axisymmetric bodies,
Dokl. Armenian AN, (1992), 93, No 1, 2327.
 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, 887901.
 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, 531539.
 Y.A. Antipov and N.Kh. Arutyunyan, Torsion of a composite sphere
with an annular or pennyshaped crack,
Mechanics of Solids (MTT), (1991), 26, No 4, 8395.
 Y.A. Antipov, Analytic solution of a twodimensional problem
for a halfplane with a crack that is close to the boundary,
Studies in elasticity and plasticity, (1990), No. 16,
1423, 204, Leningrad. Univ., Leningrad.

Y.A. Antipov and N.Kh. Arutyunyan, Torsion of an elastic ball
with a pennyshaped crack,
Mechanics of Solids (MTT), (1990), 25, No 3, 3240.
 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, 4956.
 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, 479488.
 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, 357365.
 Y.A. Antipov, Exact solution of the problem on pressing of a flat
annular punch into the halfspace, Dokl. Ukrainian AN, (1987),
A, 7, 2933.
 Y.A. Antipov, A.F. Daszczenko and A.P. Popova,
Mixed boundaryvalue problems on stress concentration in
a halfspace near a crack and a stiffener, In Solid Mechanics,
6873, Erevan (1985).
 Y.A. Antipov, Some mixed boundaryvalue problems of torsion on
stress concentration in bars, In Dynamic Systems,
6472, Kiev (1983).

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, 2742.
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