R.P. Gilbert

Personal Home Page

http://www.math.udel.edu/~gilbert/

Articles in Scholarly Journals [Incomplete List]

  1. An asymptotic model of a nonlinear adaptive elastic plate
    Mathematical and Computer Modelling, vol. 48, no. 3-4, pp. 505–517, 2008
  2. Inverse problem for wave propagation in a perturbed layered half-space
    Mathematical and Computer Modelling, vol. 45, no. 1-2, pp. 21–33, 2007
  3. Determination of the parameters of cancellous bone using high frequency acoustic measurements
    Mathematical and Computer Modelling, vol. 45, no. 3-4, pp. 281–308, 2007
  4. Homogenizing the time-harmonic acoustics of bone: The monophasic case
    Mathematical and Computer Modelling, vol. 46, no. 3-4, pp. 331–340, 2007
  5. Non-isothermal, non-Newtonian Hele–Shaw flows within Cattaneo’s heat flux law
    Mathematical and Computer Modelling, vol. 46, no. 5-6, pp. 765–775, 2007
  6. Use of specific Green's functions for solving direct problems involving a heterogeneous rigid frame porous medium slab solicited by acoustic waves
    Mathematical Methods in the Applied Sciences, vol. 30, no. 1, pp. 91–122, 2007
  7. DETERMINATION OF THE PARAMETERS OF CANCELLOUS BONE USING HIGH FREQUENCY ACOUSTIC MEASUREMENTS II: INVERSE PROBLEMS
    Journal of Computational Acoustics, vol. 15, no. 02, p. 199, 2007
  8. Numerical Homogenization of the Time-Harmonic Acoustics of Bone: The Monophasic Case
    International Journal for Multiscale Computational Engineering, vol. 5, no. 6, pp. 461–471, 2007
  9. Journal of Computational Acoustics, vol. 14, no. 2, p. 185, 2006
  10. A Prototype Homogenization Model for Acoustics of Granular Materials
    International Journal for Multiscale Computational Engineering, vol. 4, no. 5-6, pp. 585–600, 2006
  11. Vibration of an elastic plate under action of an incompressible fluid in case of N ?=?0 approximation of I. Vekua's hierarchical models§
    Applicable Analysis, vol. 85, no. 9, pp. 1177–1187, 2006
  12. Hausdorff operator on the unit polydisk in [image omitted]
    Complex Variables and Elliptic Equations, vol. 51, no. 4, pp. 329–345, 2006
  13. Identification of objects in an acoustic wave guide inversion II: Robin-Dirichlet conditions
    Mathematical Methods in the Applied Sciences, vol. 29, no. 4, pp. 401–414, 2006
  14. Homogenization of a viscoelastic matrix in linear frictional contact
    Mathematical Methods in the Applied Sciences, vol. 28, no. 3, pp. 309–328, 2005
  15. Viscosity dominated flows with temperature-dependent thermal conductivity
    Mathematical Methods in the Applied Sciences, vol. 28, no. 10, pp. 1201–1217, 2005
  16. Nonexistence of solutions to Hele-Shaw equations
    Nonlinear Analysis, vol. 63, no. 5-7, pp. 686–691, 2005
  17. Deriving the effective ultrasound equations for soft tissue interrogation
    Computers & Mathematics with Applications, vol. 49, no. 7-8, pp. 1069–1080, 2005
  18. Cylindrical vibration of an elastic cusped plate under the action of an incompressible fluid in case of N ?=?0 approximation of I. Vekuas hierarchical models
    Complex Variables, vol. 50, no. 7-11, pp. 479–496, 2005
  19. Green's function for the Helmholtz equation in a layered half-space
    Complex Variables, vol. 50, no. 7-11, pp. 869–876, 2005
  20. Journal of Computational Acoustics, vol. 13, no. 4, p. 585, 2005
  21. Journal of Computational Acoustics, vol. 12, no. 2, p. 99, 2004
  22. Effective acoustic equations for a two-phase medium with microstructure
    Mathematical and Computer Modelling, vol. 39, no. 13, pp. 1431–1448, 2004
  23. Numerical algorithm based on transmutation for solving inverse wave equation
    Mathematical and Computer Modelling, vol. 39, no. 13, pp. 1467–1476, 2004
  24. Vibration of two bonded composites: effects of the interface and distinct periodic structures
    International Journal of Solids and Structures, vol. 40, no. 12, pp. 3177–3193, 2003
  25. Transient reflection and transmission of ultrasonic wave in cancellous bone
    Applied Mathematics and Computation, vol. 142, no. 2-3, pp. 561–573, 2003
  26. Journal of Computational Acoustics, vol. 11, no. 4, p. 535, 2003
  27. Computational Results for Seamount Imaging in a Water Waveguide
    Applicable Analysis, vol. 82, no. 6, pp. 619–628, 2003
  28. Extremal solutions of a class of dynamic boundary hemivariational inequalities
    Journal of Inequalities and Applications, vol. 7, no. 4, pp. 479–502, 2002
  29. Depth sounding: an illustration of some of the pitfalls of inverse scattering problems1
    Mathematical and Computer Modelling, vol. 35, no. 11-12, pp. 1315–1354, 2002
  30. Nonlinear systems arising from nonisothermal, non-Newtonian Hele-Shaw flows in the presence of body forces and sources
    Mathematical and Computer Modelling, vol. 35, no. 13, pp. 1425–1444, 2002
  31. Unambiguous identification of the uneven boundary of a half-space probed by acoustic or electromagnetic waves
    Mathematical and Computer Modelling, vol. 36, no. 1-2, pp. 13–31, 2002
  32. Homogenizing the acoustic properties of the seabed, part II
    Mathematical and Computer Modelling, vol. 33, no. 8-9, pp. 821–841, 2001
  33. Low shear asymptotics for elastic seabeds
    Mathematical and Computer Modelling, vol. 33, no. 8-9, pp. 877–882, 2001
  34. A biographical sketch of robert carroll
    Applicable Analysis, vol. 78, no. 3, pp. 219–222, 2001
  35. The unknown object problem in a sea with sloping bottom
    Applicable Analysis, vol. 78, no. 3, pp. 497–511, 2001
  36. A two-dimensional nonlinear theory of anisotropic plates
    Mathematical and Computer Modelling, vol. 32, no. 7-8, pp. 855–875, 2000
  37. Inverse Problems, vol. 16, no. 6, pp. 1709–1726, 2000
  38. Inverse Problems, vol. 16, no. 6, pp. 1799–1811, 2000
  39. Homogenizing the acoustic properties of the seabed: Part I
    Nonlinear Analysis, vol. 40, no. 1-8, pp. 185–212, 2000
  40. Finding an inclusion in a shallow ocean using the ICBA method
    Applicable Analysis, vol. 71, no. 1, pp. 347–378, 1999
  41. Heinrich begehr on his sixtieth birthday
    Applicable Analysis, vol. 73, no. 1, pp. 1–4, 1999
  42. The unidentified object problem in a shallow ocean with a fluid-like sediment layer overlaying a rigid seabed
    Applicable Analysis, vol. 73, no. 1, pp. 5–17, 1999
  43. The unidentified object problem in a shallow ocean
    The Journal of the Acoustical Society of America, vol. 103, no. 3, p. 1320, 1998
  44. Determination of the coefficients of an elastic seabed
    Applicable Analysis, vol. 68, no. 1, pp. 75–86, 1998
  45. The fundamental singularity in a shallow ocean with an elastic seabed
    Applicable Analysis, vol. 68, no. 1, pp. 87–107, 1998
  46. Journal of Computational Acoustics, vol. 6, no. 4, p. 435, 1998
  47. Transmission loss in a shallow ocean over a two-layer seabed
    International Journal of Solids and Structures, vol. 35, no. 34-35, pp. 4779–4801, 1998
  48. Identification of a 3D void or inclusion in a plate by inversion of the diffracted wavefield
    Ultrasonics, vol. 36, no. 1-5, pp. 115–119, 1998
  49. Direct and inverse problems in ocean acoustics
    Nonlinear Analysis, vol. 30, no. 3, pp. 1535–1546, 1997
  50. Identification of a 3D object in a shallow sea from scattered sound
    Comptes Rendus de l'Acad�mie des Sciences - Series IIB - Mechanics-Physics-Chemistry-Astronomy, vol. 325, no. 7, pp. 383–389, 1997
  51. Transmission Loss in the Far Field over a One-layer Seabed Assuming the Biot Sediment Model
    ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, vol. 77, no. 2, pp. 121–135, 1997
  52. Acoustic Field in a Shallow, Stratified Ocean with a Poro-Elastic Seabed
    ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, vol. 77, no. 9, pp. 677–688, 1997
  53. Journal of Computational Acoustics, vol. 5, no. 4, p. 403, 1997
  54. A short biography of Gaetano Fichera
    Applicable Analysis, vol. 65, no. 1, pp. 1–2, 1997
  55. Green' function representation for acoustic pressure over a poroelastic seabed
    Applicable Analysis, vol. 65, no. 1, pp. 57–68, 1997
  56. The coefficient problem for a shallow ocean with an unknown ihhomogeneity and an elastic seabed
    Applicable Analysis, vol. 63, no. 1, pp. 77–86, 1996
  57. Journal of Computational Acoustics, vol. 4, no. 1, p. 29, 1996
  58. Nonisothermal, nonNewtonian hele-shaw flows, Part II: Asymptotics and existence of weak solutions
    Nonlinear Analysis, vol. 27, no. 5, pp. 539–559, 1996
  59. Biography of professor alan jeffrey
    Applicable Analysis, vol. 57, no. 1, pp. 1–1, 1995
  60. Journal of Computational Acoustics, vol. 1, no. 1, p. 31, 1993
  61. Journal of Computational Acoustics, vol. 1, no. 2, p. 229, 1993
  62. Two free boundary problems occuring in planar filtrations
    Nonlinear Analysis, vol. 21, no. 11, pp. 859–868, 1993
  63. An Inverse Problem for Harmonic Acoustics in Stratified Oceans
    Journal of Mathematical Analysis and Applications, vol. 176, no. 1, pp. 121–137, 1993
  64. Some Initial Boundary Value Problems for a Nonlinear Pseudoparabolic System
    Mathematische Nachrichten, vol. 163, no. 1, pp. 27–34, 1993
  65. Dense sets and the projection theorem for acoustic harmonic waves in a homogeneous finite depth ocean
    Mathematical Methods in the Applied Sciences, vol. 12, no. 1, pp. 69–76, 1990
  66. The propagation problem and far-field patterns in a stratified finite-depth ocean
    Mathematical Methods in the Applied Sciences, vol. 12, no. 3, pp. 199–208, 1990
  67. A solution to the equations of shell theory
    Mathematical Methods in the Applied Sciences, vol. 12, no. 4, pp. 341–363, 1990
  68. Anisotropic Hele-Shaw flows
    Mathematical Methods in the Applied Sciences, vol. 11, no. 4, pp. 417–429, 1989
  69. Free boundary problems occurring in planar fluid dynamics
    Nonlinear Analysis, vol. 13, no. 3, pp. 285–303, 1989
  70. Starting fields and far fields in ocean acoustics
    Wave Motion, vol. 11, no. 6, pp. 507–524, 1989
  71. Construction of approximations to acoustic Green's functions for nonhomogeneous oceans using transmutation
    Wave Motion, vol. 10, no. 3, pp. 285–297, 1988
  72. A moving boundary problem associated with flow through a porous medium
    Nonlinear Analysis, vol. 12, no. 2, pp. 109–119, 1988
  73. Pure bending problem for a vibrating elastic plate with non-uniform temperature
    Journal of Elasticity, vol. 20, no. 2, pp. 93–112, 1988
  74. On the approximation of acceleration waves in rods
    International Journal of Non-Linear Mechanics, vol. 22, no. 3, pp. 209–215, 1987
  75. The boundary integral method for two-dimensional orthotropic materials
    Journal of Elasticity, vol. 18, no. 1, pp. 61–82, 1987
  76. Non-newtonian Hele-Shaw flows in n ?2 dimensions
    Nonlinear Analysis, vol. 11, no. 1, pp. 17–47, 1987
  77. Distribution-Free Confidence Intervals for Pr(X 1 < X 2 )
    Biometrics, vol. 43, no. 1, p. 71, 1987
  78. Hele-Shaw type flows in ?n
    Nonlinear Analysis, vol. 10, no. 1, pp. 65–85, 1986
  79. A transmutation approach to underwater sound propagation
    Wave Motion, vol. 8, no. 5, pp. 383–397, 1986
  80. The two-dimensional, linear, orthotropic plate: The traction problem
    Mathematical Methods in the Applied Sciences, vol. 8, no. 1, pp. 102–116, 1986
  81. Function theoretic solutions to problems of orthotropic elasticity
    Journal of Elasticity, vol. 15, no. 2, pp. 143–154, 1985
  82. Constructive methods for fourth-order elliptic equations
    Journal of Approximation Theory, vol. 44, no. 1, pp. 55–68, 1985
  83. A Boundary-Layer Theory for the Orthotropic Plate
    ZAMM - Zeitschrift für Angewandte Mathematik und Mechanik, vol. 63, no. 6, pp. 229–237, 1983
  84. A reactive shock in a polytropic gas*1
    Journal of Mathematical Analysis and Applications, vol. 89, no. 1, pp. 193–202, 1982
  85. A Lewy-type reflection principle for pseudoparabolic equations
    Journal of Differential Equations, vol. 37, no. 2, pp. 261–284, 1980
  86. On Riemann boundary value problems for certain linear elliptic systems in the plane
    Journal of Differential Equations, vol. 32, no. 1, pp. 1–14, 1979
  87. On a class of boundary value problems for a composite system of first order differential equations
    Journal of Approximation Theory, vol. 25, no. 2, pp. 105–119, 1979
  88. BERGMAN Type Operators for Pseudoparabolic Equations in several Space Variables
    Mathematische Nachrichten, vol. 76, no. 1, pp. 61–68, 1977
  89. Constructive Methods for Solving ?42u+A?4ut+But+C?4u+Du = 0
    Mathematische Nachrichten, vol. 80, no. 1, pp. 105–113, 1977
  90. Hilbert function modules with reproducing kernels
    Nonlinear Analysis, vol. 1, no. 2, pp. 135–150, 1977
  91. Hypercomplex Function Theory in the Sense of L. BERS
    Mathematische Nachrichten, vol. 72, no. 1, pp. 187–200, 1976
  92. On a normal form for second order elliptic equations and constructive methods for Dirichlet's problem
    Mathematische Nachrichten, vol. 67, no. 6-9, pp. 139–143, 1975
  93. A Function Theoretic Method for ?32u +Q(x)u = 0
    Mathematische Nachrichten, vol. 67, no. 10-14, pp. 199–212, 1975
  94. A function theoretic method for? 4 2 u+Q(x)u=0
    Annali di Matematica Pura ed Applicata, Series 4, vol. 104, no. 1, pp. 31–42, 1975
  95. Generalized Hypercomplex Function Theory
    Transactions of the American Mathematical Society, vol. 195, p. 1, 1974
  96. Corrigendum
    Archive for Rational Mechanics and Analysis, vol. 48, no. 5, pp. 397–397, 1972
  97. Integral operators and complete families of solutions for $$\Delta _{p + 2}^2 u\left( {\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{x} } \right) + A\left( {r^2 } \right)\Delta _{p + 2} u\left( {\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{x} } \right) + B(r^2 )u\left( {\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{x} } \right) = 0$$
    Archive for Rational Mechanics and Analysis, vol. 43, no. 1, 1971
  98. The scope of the function theoretic approach for equations permitting a separation of variables
    Journal of Mathematical Analysis and Applications, vol. 34, no. 3, pp. 671–684, 1971
  99. SIAM Journal on Mathematical Analysis, vol. 2, no. 1, Article ID 0502002, 1971
  100. SIAM Journal on Mathematical Analysis, vol. 2, no. 1, Article ID 0502011, 1971
  101. SIAM Journal on Mathematical Analysis, vol. 1, no. 1, Article ID 0501010, 1970
  102. A Contribution to the Vekua-Rellich Theory of Metaharmonic Functions
    American Journal of Mathematics, vol. 92, no. 3, p. 525, 1970
  103. SIAM Journal on Applied Mathematics, vol. 16, no. 1, Article ID 0116002, 1968
  104. Representation Functions of the Group of Motions of Clifford Space
    Journal of Mathematical Physics, vol. 8, no. 1, p. 135, 1967
  105. Role of the Integral-Operator Method in the Theory of Potential Scattering
    Journal of Mathematical Physics, vol. 8, no. 1, p. 141, 1967
  106. A New Method in the Theory of Potential Scattering
    Journal of Mathematical Physics, vol. 7, no. 3, p. 431, 1966
  107. A second order, non-linear elliptic boundary value problem with generalized Goursat data
    Annali di Matematica Pura ed Applicata, Series 4, vol. 72, no. 1, pp. 325–341, 1966
  108. Singularities of Analytic Functions Having Integral Representations, with a Remark about the Elastic Unitarity Integral
    Journal of Mathematical Physics, vol. 6, no. 7, p. 1157, 1965
  109. Analytic Properties of the Elastic Unitarity Integral
    Journal of Mathematical Physics, vol. 6, no. 11, p. 1626, 1965
  110. Bergman's Integral Operator Method in Generalized Axially Symmetric Potential Theory
    Journal of Mathematical Physics, vol. 5, no. 7, p. 983, 1964
  111. Poisson's equation and generalized axially symmetric potential theory
    Annali di Matematica Pura ed Applicata, Series 4, vol. 62, no. 1, pp. 337–348, 1963
  112. On the geometric character of singularity manifolds for harmonic functions in three variables: I
    Archive for Rational Mechanics and Analysis, vol. 9, no. 1, 1962
  113. A Note on the Singularities of Harmonic Functions in Three Variables
    Proceedings of the American Mathematical Society, vol. 13, no. 2, p. 229, 1962
  114. Some Properties of Generalized Axially Symmetric Potentials
    American Journal of Mathematics, vol. 84, no. 3, p. 475, 1962
  115. On the theory of hot-water drives
    Zeitschrift für angewandte Mathematik und Physik ZAMP, vol. 12, no. 6, pp. 489–496, 1961
  116. A further note on a two-dimensional free-boundary problem
    Zeitschrift für angewandte Mathematik und Physik ZAMP, vol. 12, no. 1, pp. 69–70, 1961
  117. On a two-dimensional free-boundary problem
    Zeitschrift für angewandte Mathematik und Physik ZAMP, vol. 11, no. 5, pp. 341–355, 1960
  118. Reversein situ combustion
    Zeitschrift für angewandte Mathematik und Physik ZAMP, vol. 10, no. 6, pp. 544–551, 1959