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

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.