Dr. Yongzhi Steve Xu

Professor of
Mathematics

Department of
Mathematics, University of Louisville, Louisville, KY 40292

Professional
Experience

Professor, University of Louisville,
2004 -- current, Teaching and research.

Professor, University of Tennessee at
Chattanooga, 2000 -- 2004, Teaching and research.

Associate Professor, University of
Tennessee at Chattanooga, 1997 -- 2000, Teaching and research.

Assistant Professor, University of
Tennessee at Chattanooga, 1995 -- 1997, Teaching and research.

Assistant Professor, Georgetown
University, 1992 -- 1995, Teaching and research.

Postdoctorate fellow,
Institute for Mathematics and its Applications, University of Minnesota, 1990
-- 1992, Research and other activities in industrial mathematics.

Member
of editorial boards

Editor-in-Chief of Applicable
Analysis

Editor-in-Chief of Complex Variables and Elliptic
Equations

Mathematical
Methods in Applied Sciences

Taiwanese Journal of
Mathematics

Education

Industrial Postdoc,
(Advisor Avner Friedman), Institute for Mathematics
and its Applications, University of Minnesota, 1990 - 1992, Applied
Mathematics.

Ph. D., (Advisor Robert Gilbert),
University of Delaware, 1990,
Mathematics.

M. S., (Advisor Wei Lin) Zhongshan University, Guangzhou, China, 1984, Mathematics.

B. S., Zhongshan
University, Guangzhou, China, 1982, Mathematics.

Publications

Books

1.
Marine
Acoustics: Direct and Inverse Problems, by James. Buchanan, Robert Gilbert,
Armand. Wirgin and Yongzhi Xu, SIAM, 2004.

2.
Direct
and Inverse Problems of Mathematical Physics, Edited by Robert P. Gilbert, Joli Kajiwara and Yongzhi S. Xu, Kluwer Academic Publishers, 1999.

3.
Complex
Analysis and Computer Algebra --- Recent Developments, Edited by Robert P.
Gilbert, Joli Kajiwara and Yongzhi S. Xu, Kluwer Academic Publishers, 1999.

Papers

1.
``Cauchy
type integral of (\lambda, k) bi-analytic functions and Riemann problem,'' Acta Scientiarum Naturalium Universitatis Sunyatseni, 3 (1984), 142 - 155.

2.
``
Riemann - Hilbert problem and the second problem for a class of second order
elliptic systems,'' J. Math. Res. Exposition, (1986), no. 1, 86 - 94.

3.
``Generalized
(\lambda, k) bi-analytic functions and Riemann - Hilbert problem for a class of
nonlinear second order elliptic systems,'' Complex Variables Theory Appl. 8
(1987), no. 1-2, 103 - 121.

4.
``The
existence and uniqueness of solutions of Dirichlet
problems for second order linear elliptic systems in Petrovskii's
sense,'' (Chinese), Acta Sci. Natur.
Univ. Sunyatseni, 4 (1987), 21-28, (Math. Review 89i:
35046), (with Chen, Mai).

5.
``Construction
of approximation to acoustic Green's functions for nonhomogeneous
ocean using transmutations,'' Wave Motion, 10, (1988) 285-297, (with R. Gilbert
and D. Wood).

6.
``Starting
fields and far fields in ocean acoustics," Wave Motion, 11, 507-524,
(1989), (with R. Gilbert).

7.
``The
propagation problem and far-field patterns in a stratified finite depth
ocean,'' Mathematical Methods in the Applied Sciences, Vol. 12, 199-208,
(1989), (with R. Gilbert).

8.
``A
Function theory for thin elastic shells,'' J. of Elasticity, 22, (1989), 81-93,
(with R. Gilbert).

9.
``An
optimal control problem for Helmholtz equation in stratified shallow oceans,''
Mathematical Methods in the Applied Sciences, Vol. 13 (1990) 405-419.

10. ``Dirichlet problem for a class of second order nonlinear
elliptic systems,'' Complex Variables, Vol. 15, 4 (1990) 241-258.

11. ``The
propagating solution and far field patterns for acoustic harmonic waves in a
finite depth ocean," Applicable Analysis, Vol.35, 1-4, (1990), 129-151.

12. ``Underwater
acoustics for Submersibles,'' Ocean Resources, D.A.Ardus
and M.A.Champ (eds.), Vol. 2, 135-146, (1990), (with R.Gilbert and D. Wood).

13. ``Dense sets and
the projection theorem for acoustic harmonic waves in homogeneous finite depth
ocean,'' Mathematical Methods in the Applied Sciences, Vol. 12, 69-76, (1990)
(with R. Gilbert).

14. ``An injective
far-field pattern operator and inverse scattering problem in a finite depth
ocean'', Proceedings of the Edinburgh Mathematical Society, 34 (1991) 295-311.

15. ``Shape
reconstruction from far-field patterns in a stratified ocean,'' Automatic
Object Recognition, ed. Firooz Sadjadi,
SPIE, 78-85, (1991).

16. ``An
approximation scheme for three-dimensional scattered wave and its propagating
far-field pattern in a finite depth ocean,'' Z. Angew.
Math. Mechanik, Vol. 72 (1992) 10, 459-480, (with R.
Gilbert and P. Thejll).

17. ``Acoustic waves
and far-field patterns in two dimensional oceans with porous-elastic seabeds,'' (with R. Gilbert), Results in Mathematics, Vol.
22 (1992) 685-700.

18. ``Source
localization processing in perturbed waveguides,'' (with Y. Yan) J. Acous. Soc. Ame., Vol. 91(8),
1992.

19. ``Generalized Herglotz functions and inverse scattering problem in a finite
depth ocean,'' (with R. Gilbert), Invariant Imbedding and Inverse Problems,
SIAM Proceedings in Applied Mathematics 63, Ed. J. Corones,
et al. 1992.

20. ``Scattering of
acoustic wave by obstacle in stratified medium,'' Partial Differential
Equations with Real Analysis Ed. H. Begehr, A.
Jeffrey, Pitman Research Notes in Mathematics Series 263, (1992) 147-168.

21. ``Scattering of
acoustic waves by an ellipse in a shallow ocean,'' (with R. Gilbert), Advances
in Computer Methods for Partial Differential Equations VII, R. Vichnevetsky, D. Knight and G. Richter (Editors), IMACS,
(1992), 287-293.

22. ``An inverse
problem for harmonic acoustics in stratified oceans,'' (with R. Gilbert), J.
Math. Anal. Appl., Vol. 176, No. 1, (1993) 121-137.

23. ``Decoupling of
the quasistatic system of the thermoelasticity
on the unit disk,'' (with Peter Shi), J. of Elasticity, 31 (1993) 209-218.

24. ``An approximate
boundary integral equation method for acoustic scattering in shallow oceans,''
(with Y. Yan), J. of Computational Acoustics, Vol. 1, No. 1 (1993).

25. ``Direct and
inverse scattering of time harmonic acoustic waves in inhomogeneous shallow
ocean,'' (with T. C. Poling and T. Brundage),
Computational Acoustics, Acoustic Propagation, Ed. D. Lee et al, North-Holland,
21-43, (1993).

26. ``An unidentified
inclusion problem for a shallow ocean I: Construction of the Green's
function,'' (with R. Gilbert and K. Khashanah),
Computational Acoustics, Acoustic Propagation, Ed. D. Lee et al, North-Holland,
1-20, (1993).

27. ``A boundary
integral method for acoustic source localization in a waveguide with
inclusion,'' (with Y. Yan), J. of Computational Acoustics, Vol. 2, No. 2 (1994)
133-145.

28. ``Continuous
wave mode structure and constraint beamforming in a
waveguide with unknown large inclusions,'' J. Acous.
Soc. Ame., Vol 95(1),
January (1994), 1-13.

29. ``Reciprocity
relations and completeness of far-field pattern vectors for obstacle scattering
of acoustic wave in a stratified medium,'' Math. Meth. in Appl. Sciences, Vol.
18, 51-66 (1995).

30. ``Radiation
condition and scattering problem for time-harmonic acoustic waves in a
stratified medium with non-homogeneity,'' IMA J. of Appl. Math., 54 (1995),
9-29.

31. ``Inverse
scattering of acoustic waves in an ocean with ice cover'', (with B. Belinskiy and J. Dauer), Applicable
Analysis, Vol. 61, (1996), 255-283.

32. ``The
coefficient problem for a shallow ocean with an unknown inhomogeneity
and an elastic seabed'', (with R. Gilbert), Applicable Analysis, Vol. 63,
77-86, (1996).

33. ``Normal modes
analysis for sound waves in an ocean with an ice cap and a perfectly reflecting
bottom'', (with W. Lin and Y. Zhao), Applicable Analysis, Vol. 63, (1996).

34. ``A sea-mount
problem'' (with R. Gilbert), SIAM special issue on the occasion of Professor Ivar Stakgold's 70th birthday,
Nonlinear Problems in Applied Mathematics, Editor T. Angell et al, (1996),
140-149.

35. ``Analytical
methods for acoustic seabed exploration'', (with M. Gaer
and R. Gilbert), Oceans '95 MTS/IEEE Proceedings, (1996), 214-220.

36. ``Object shape
determination using incomplete data in a stratified medium'', Automatic Object
Recognition, Firooz A. Sadjadi,
Editor, Proc. SPIE 2756, (1996), 164-173.

37. ``Identification
of a 3D object in a shallow sea from scattered sound'', (with R. Gilbert, T. Scotti and A. Wirgin), Compte Rendues, Acad. Sci. Paris,
serie IIb, 325, 383-389,
1997

38. ``Green's
function for acoustic pressure over a poroelastic
seabed'' (with J. Buchanan and R. Gilbert), Applicable Analysis, Vol. 65,
(1997), 57-68.

39. ``A Note on the
Uniqueness of the Propagating Solution for Acoustic Waves in a Finite Depth
Ocean'', , Applicable Analysis, Vol. 67, (1997), 201-204.

40. ``The
unidentified object problem in a shallow ocean'', (with R. Gilbert, T. Scotti and A. Wirgin), J.
Acoustic Society of America, 103 (3), (1998), 1320-1327.

41. ``An inverse
obstacle scattering problem in a stratified medium'', Applicable Analysis, Vol.
68(3-4), 61-2280, (1998).

42. ``Some Inverse
Problems in Stratified Media'', Generalized Analytic Functions, ed. H. florian et al., Kluwer Academic
Publishers, 255-264, (1998).

43. ``Identification
of a 3D void or inclusion in a plate by inversion of diffracted wavefield'', (with R.P. Gilbert, T. Scotti,
and A. Wirgin), Ultrasonics,
36, (1998), 115-119.

44. ``Inverse
acoustic scattering problems in ocean environments'', J. of Computational
Acoustics, Vol. 7, No. 2(1999), 111-132.

45. ``The
unidentified object problem in a shallow ocean with a fluid-like sediment layer
overlying a rigid seabed'', (joint with Buchanan, Gilbert and Wirgin), Applicable Analysis, Vol. 73(1-2), 5-17, (1999).

46. ``An inverse
problem for the quasistatic thermoelastic
system on the unit disk'', Applicable Analysis, Vol. 73(1-2), 295-305, (1999).

47. ``Inverse
scattering problems in ocean environments'', Theoretical and Computational
Acoustics '97, Teng, Shang, Pao,
Schultz and Pierce (Editors), World Scientific, (1999), 217-228.

48. ''Inverse
scattering method for imaging objects in ocean environments'', Proceeding of
PIEMA99, Clermont-Ferrand, France, (1999).

49. ``Generalized
dual space indicator method for underwater imaging'', (joint with Mawata and Lin), Inverse Problems, 16(2000) 1761-1776.

50. ``Identification,
by the intersecting canonical domain method, of the size shape and depth of a
soft body of revolution located within an acoustic waveguide,'' (joint with
Buchanan, Gilbert and Wirgin), Inverse Problems,
16(2000) 1709-1726.

51. ``Acoustic
imaging in a shallow ocean with a thin ice cap,'' (joint with Gilbert), Inverse
Problems 16(2000) 1799-1811.

52. ``Identification
of acoustically soft solids of revolution in a waveguide using the ICBA
method'', (with Buchanan, Gilbert and Wirgin),
Analytical and Computational Methods in Scattering Theory and Applied
Mathematics, CRC Press LLC, 2000, 27-36.

53. ``Determination
of a distributed inhomogeneity in a two-layered
waveguide from scattered sound'', (joint with Gilbert and Mawata),
Direct and Inverse Problems of Mathematical Physics, ed. R. Gilbert, et al., Kluwer Academic Publishers, 2000, 107-124.

54. ``Generalized
dual space indicator method for inverse scattering problems in underwater acoustics'',
Mathematical and numerical aspects of wave propagation, (Santiago de Compostela, 2000), 543-547, SIAM, Philadelphia, PA, 2000.

55. ``Generalized
Dual Space Indicator Method for Imaging Obstacles in a Homogeneous Medium'',
(joint with Mawata and Lin), Proceedings of the
Second ISAAC Congress, Vol. 2 (Fukuoka, 1999), 1599-1606., Int. Soc. Anal.
Appl. Comput., 8, Kluwer
Acad. Publ., Dordrecht, 2000.

56. ``Continuity and
determination of parameters for quasistatic thermoelastic system'', (joint with He), Proceedings of the
Second ISAAC Congress, Vol. 2 (Fukuoka, 1999), 1585--1597, Int. Soc. Anal.
Appl. Comput., 8, Kluwer
Acad. Publ., Dordrecht, 2000.

57. ``Determination
of a buried object in a two-layered shallow ocean'' (joint with Gilbert and Wirby), Vol. 9, No. 3 , J. of Computational Acoustics,
(2001) 1025-1037.

58. ``The unknown
object problem in a sea with sloping bottom'', (with R. Gilbert and M. Ou), Applicable Analysis, Vol. 78, No. 3-4, (2001),
497-511.

59. ``The Seamount
on a sloping seabed problem'', (with R. Gilbert and M. Ou),
Differential Equations and Nonlinear Mechanics, Ed. K. Vajravelu,
Kluwer Academic Publishers, (2001), 101-112.

60. ``Depth
sounding: an illustration of some of the pitfalls of inverse scattering
problems'', (with Buchanan, J., Gilbert, R., and Wirgin,
A.) Math. Comput.
35 (2002), no. 11-12, 1315--1354.

61. ``Unambiguous
identification of the uneven boundary of a half-space probed by acoustic or
electromagnetic waves", (joint with J. Buchanan, R. Gilbert and A. Wirgin), Mathematical and Computer Modelling,
36 (2002), no. 1-2, 13-31.

62. ``Transient
Reflection and Transmission of Ultrasonic Wave in Cancellous
Bone", (joint with J. Buchanan, R. Gilbert and A. Wirgin),
Applied mathematics and computation. 142, no. 2, (2003): 561-575.

63. “Computational
Results for Obstacle Inverse Scattering in a Water Waveguide’’, (joint with R.
Gilbert), Applicable Analysis, Vol 82, No. 6 (2003),
619-628.

64. ``Transmission
of ultrasonic wave in cancellous bone and evaluation
of osteoporosis'', Acoustics, Mechanic, and the Related Topics of Mathematical
Analysis, Ed. A. Wirgin, World Scientific, (2003).

65. “A free boundary
problem model of ductal carcinoma in situ,” Discrete
and Continous dynamical systems - Series B, Vol. 4,
No. 1 (2004), 337-348.

66. “Marine
Acoustics: Direct and Inverse Scattering of Waves”, (with J. BUCHANAN, R.
Gilbert, A. Wirgan), Other Titles in Applied
Mathematics, SIAM, 2004.

67. Transmitted wave
in a poroelastic medium and its application in
evaluation of osteoporosis, Proceeding of Dynamic Systems and Applications,
Dynamic Publishers, Vol. 4, (2004), 662-669.

68. "Viscosity
Dominated flows with temperature-dependent Thermal Conductivity," (with R.
Gilbert and M. Fang), Mathematical
Methods in Applied Sciences, Volume 28, Issue 10, (2005), 1201-1217.

69. ``Green's
function for Holmholtz equation in a Layered
Half-Space", (with R. Gilbert), Complex Variables, Vol. 50, No. 7-11,
(2005), 869-876.

70. "A
Mathematical Model of Ductal Carcinoma in Situ and
its Characteristic Patterns," Advances in Analysis, edited by H. Begehr, etc, World Scientific, 2005, 365-374.

71. ``Ultrasound as
a Diagnostic Tool to Determine Osteoporosis", (with Buchanan and Gilbert),
Advances in Analysis, edited by H. Begehr, etc, World
Scientific, 2005, 345-354.

72. Focused
Ultrasonic Wave in Submerged Cancellous Bone, Journal
of Computational Acoustics, (with R. Gilbert and W. Lin), Vol. 13, No. 4 (2005)
585-601.

73. Acoustic
identification of a poroelastic cylinder, (with A. Wirgin, et al.)
Proceedings on the Acoustics of Poro-Elastic
Materials, Lyon, France, 2005, 211-218.

74. A mathematical
model for evaluation of osteoporosis, (with R. Gilbert, A. Wirgin and S. Zhang,) Proceedings on the Acoustics of Poro-Elastic Materials, Lyon, France, 2005, 203-210.

75. A free boundary
problem of parabolic complex equation, Complex Variables and Elliptic
Equations, Vol. 51, Nos. 8-11, 2006, Pages 945-951.

76. A free boundary
problem of diffusion equation with integral condition, Applicable Analysis,
Vol. 85, No. 9, 2006, 1143-1152.

77. Inverse problem for
wave propagation in a perturbed layered half-space, (wirh
R. Gilbert and Klaus Hackl), Mathematical and Computer Modeling, 45 (1-2), 2007, 21-33.

78. Use of specific
Green's functions for solving direct problems involving a heterogeneous rigid
frame porous medium slab solicited by acoustic waves, (with J. Groby, L. Ryck , P. Leclaire, A. Wirgin, W. Lauriks and R.
Gilbert), Math.Meth.Appl.Sci, Vol. 30, No.1, 2007,
91-122.

79. Computing
porosity of cancellous bone using ultrasonic waves,
(with R. Gilbert and S. Zhang), Journal
of Applied Functional Analysis, 2 (2) 2007, 185-196.

80. Riemann Problem
and Inverse Riemann Problem of ($\lambda$, 1) Bi-analytic Functions, Complex
Variables and Elliptic Equations, 2007.

81. John M. Cochran
and Yongzhi Xu, Analysis of
Linearized Version of Active Contours Without
Gradient, Applicable Analysis,Vol. Issue8,2008

82. Erick Ogam, Armand Wirgin, Stefan
Schneider, Z.E.A. Fellah, Yongzhi Xu,
Recovery elastic parameters of cellular
materials by inversion of vibrational data, Journal of Sound and Vibration, Volume
313, Issues 3-5, 17 June 2008, Pages 525-543

83. Xiaoling Li, Yuying Qiao and Yongzhi Xu, Clifford Analysis with Higher Order Kernel
over Unbounded Domains, Complex Variables and Elliptic Equations, Volume 53,
Issue 6, 2008, 585-605.

84. Yongzhi Xu, Scattered Waves Through a Waveguide From a Half-Opened
Space; Discrete and Computational Mathematics, Chapter 21, Editors: Fengshan Liu et al. Nova Science Pub Inc, 2008, pp 309-322.

85. R. Gilbert, Y.
Xu and S. Zhang, A mathematical model for the evaluation of osteoporosis ,
Discrete and Computational Mathematics, Chapter 1, Editors: Fengshan
Liu et al. Nova Science Pub Inc, 2008, pp 1-16.