R.P. Gilbert
Personal Home Page
http://www.math.udel.edu/~gilbert/
Articles in Scholarly Journals [Incomplete List]
- An asymptotic model of a nonlinear adaptive elastic plate
Mathematical and Computer Modelling, vol. 48, no. 3-4, pp. 505–517, 2008 - Inverse problem for wave propagation in a perturbed layered half-space
Mathematical and Computer Modelling, vol. 45, no. 1-2, pp. 21–33, 2007 - 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 - Homogenizing the time-harmonic acoustics of bone: The monophasic case
Mathematical and Computer Modelling, vol. 46, no. 3-4, pp. 331–340, 2007 - 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 - 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 - 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 - 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 - Journal of Computational Acoustics, vol. 14, no. 2, p. 185, 2006
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A Prototype Homogenization Model for Acoustics of Granular Materials
International Journal for Multiscale Computational Engineering, vol. 4, no. 5-6, pp. 585–600, 2006 - 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 - Hausdorff operator on the unit polydisk in [image omitted]
Complex Variables and Elliptic Equations, vol. 51, no. 4, pp. 329–345, 2006 - 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 - Homogenization of a viscoelastic matrix in linear frictional contact
Mathematical Methods in the Applied Sciences, vol. 28, no. 3, pp. 309–328, 2005 - Viscosity dominated flows with temperature-dependent thermal conductivity
Mathematical Methods in the Applied Sciences, vol. 28, no. 10, pp. 1201–1217, 2005 - Nonexistence of solutions to Hele-Shaw equations
Nonlinear Analysis, vol. 63, no. 5-7, pp. 686–691, 2005 - Deriving the effective ultrasound equations for soft tissue interrogation
Computers & Mathematics with Applications, vol. 49, no. 7-8, pp. 1069–1080, 2005 - 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 - Green's function for the Helmholtz equation in a layered half-space
Complex Variables, vol. 50, no. 7-11, pp. 869–876, 2005 - Journal of Computational Acoustics, vol. 13, no. 4, p. 585, 2005
- Journal of Computational Acoustics, vol. 12, no. 2, p. 99, 2004
- Effective acoustic equations for a two-phase medium with microstructure
Mathematical and Computer Modelling, vol. 39, no. 13, pp. 1431–1448, 2004 - Numerical algorithm based on transmutation for solving inverse wave equation
Mathematical and Computer Modelling, vol. 39, no. 13, pp. 1467–1476, 2004 - 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 - Transient reflection and transmission of ultrasonic wave in cancellous bone
Applied Mathematics and Computation, vol. 142, no. 2-3, pp. 561–573, 2003 - Journal of Computational Acoustics, vol. 11, no. 4, p. 535, 2003
- Computational Results for Seamount Imaging in a Water Waveguide
Applicable Analysis, vol. 82, no. 6, pp. 619–628, 2003 - Extremal solutions of a class of dynamic boundary hemivariational inequalities
Journal of Inequalities and Applications, vol. 7, no. 4, pp. 479–502, 2002 - 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 - 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 - 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 - Homogenizing the acoustic properties of the seabed, part II
Mathematical and Computer Modelling, vol. 33, no. 8-9, pp. 821–841, 2001 - Low shear asymptotics for elastic seabeds
Mathematical and Computer Modelling, vol. 33, no. 8-9, pp. 877–882, 2001 - A biographical sketch of robert carroll
Applicable Analysis, vol. 78, no. 3, pp. 219–222, 2001 - The unknown object problem in a sea with sloping bottom
Applicable Analysis, vol. 78, no. 3, pp. 497–511, 2001 - A two-dimensional nonlinear theory of anisotropic plates
Mathematical and Computer Modelling, vol. 32, no. 7-8, pp. 855–875, 2000 - Inverse Problems, vol. 16, no. 6, pp. 1709–1726, 2000
- Inverse Problems, vol. 16, no. 6, pp. 1799–1811, 2000
- Homogenizing the acoustic properties of the seabed: Part I
Nonlinear Analysis, vol. 40, no. 1-8, pp. 185–212, 2000 - Finding an inclusion in a shallow ocean using the ICBA method
Applicable Analysis, vol. 71, no. 1, pp. 347–378, 1999 - Heinrich begehr on his sixtieth birthday
Applicable Analysis, vol. 73, no. 1, pp. 1–4, 1999 - 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 - The unidentified object problem in a shallow ocean
The Journal of the Acoustical Society of America, vol. 103, no. 3, p. 1320, 1998 - Determination of the coefficients of an elastic seabed
Applicable Analysis, vol. 68, no. 1, pp. 75–86, 1998 - The fundamental singularity in a shallow ocean with an elastic seabed
Applicable Analysis, vol. 68, no. 1, pp. 87–107, 1998 - Journal of Computational Acoustics, vol. 6, no. 4, p. 435, 1998
- 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 - 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 - Direct and inverse problems in ocean acoustics
Nonlinear Analysis, vol. 30, no. 3, pp. 1535–1546, 1997 - 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 - 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 - 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 - Journal of Computational Acoustics, vol. 5, no. 4, p. 403, 1997
- A short biography of Gaetano Fichera
Applicable Analysis, vol. 65, no. 1, pp. 1–2, 1997 - Green' function representation for acoustic pressure over a poroelastic seabed
Applicable Analysis, vol. 65, no. 1, pp. 57–68, 1997 - 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 - Journal of Computational Acoustics, vol. 4, no. 1, p. 29, 1996
- Nonisothermal, nonNewtonian hele-shaw flows, Part II: Asymptotics and existence of weak solutions
Nonlinear Analysis, vol. 27, no. 5, pp. 539–559, 1996 - Biography of professor alan jeffrey
Applicable Analysis, vol. 57, no. 1, pp. 1–1, 1995 - Journal of Computational Acoustics, vol. 1, no. 1, p. 31, 1993
- Journal of Computational Acoustics, vol. 1, no. 2, p. 229, 1993
- Two free boundary problems occuring in planar filtrations
Nonlinear Analysis, vol. 21, no. 11, pp. 859–868, 1993 - An Inverse Problem for Harmonic Acoustics in Stratified Oceans
Journal of Mathematical Analysis and Applications, vol. 176, no. 1, pp. 121–137, 1993 - Some Initial Boundary Value Problems for a Nonlinear Pseudoparabolic System
Mathematische Nachrichten, vol. 163, no. 1, pp. 27–34, 1993 - 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 - 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 - A solution to the equations of shell theory
Mathematical Methods in the Applied Sciences, vol. 12, no. 4, pp. 341–363, 1990 - Anisotropic Hele-Shaw flows
Mathematical Methods in the Applied Sciences, vol. 11, no. 4, pp. 417–429, 1989 - Free boundary problems occurring in planar fluid dynamics
Nonlinear Analysis, vol. 13, no. 3, pp. 285–303, 1989 - Starting fields and far fields in ocean acoustics
Wave Motion, vol. 11, no. 6, pp. 507–524, 1989 - Construction of approximations to acoustic Green's functions for nonhomogeneous oceans using transmutation
Wave Motion, vol. 10, no. 3, pp. 285–297, 1988 - A moving boundary problem associated with flow through a porous medium
Nonlinear Analysis, vol. 12, no. 2, pp. 109–119, 1988 - Pure bending problem for a vibrating elastic plate with non-uniform temperature
Journal of Elasticity, vol. 20, no. 2, pp. 93–112, 1988 - On the approximation of acceleration waves in rods
International Journal of Non-Linear Mechanics, vol. 22, no. 3, pp. 209–215, 1987 - The boundary integral method for two-dimensional orthotropic materials
Journal of Elasticity, vol. 18, no. 1, pp. 61–82, 1987 - Non-newtonian Hele-Shaw flows in n ?2 dimensions
Nonlinear Analysis, vol. 11, no. 1, pp. 17–47, 1987 - Distribution-Free Confidence Intervals for Pr(X 1 < X 2 )
Biometrics, vol. 43, no. 1, p. 71, 1987 - Hele-Shaw type flows in ?n
Nonlinear Analysis, vol. 10, no. 1, pp. 65–85, 1986 - A transmutation approach to underwater sound propagation
Wave Motion, vol. 8, no. 5, pp. 383–397, 1986 - The two-dimensional, linear, orthotropic plate: The traction problem
Mathematical Methods in the Applied Sciences, vol. 8, no. 1, pp. 102–116, 1986 - Function theoretic solutions to problems of orthotropic elasticity
Journal of Elasticity, vol. 15, no. 2, pp. 143–154, 1985 - Constructive methods for fourth-order elliptic equations
Journal of Approximation Theory, vol. 44, no. 1, pp. 55–68, 1985 - A Boundary-Layer Theory for the Orthotropic Plate
ZAMM - Zeitschrift für Angewandte Mathematik und Mechanik, vol. 63, no. 6, pp. 229–237, 1983 - A reactive shock in a polytropic gas*1
Journal of Mathematical Analysis and Applications, vol. 89, no. 1, pp. 193–202, 1982 - A Lewy-type reflection principle for pseudoparabolic equations
Journal of Differential Equations, vol. 37, no. 2, pp. 261–284, 1980 - 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 - 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 - BERGMAN Type Operators for Pseudoparabolic Equations in several Space Variables
Mathematische Nachrichten, vol. 76, no. 1, pp. 61–68, 1977 - Constructive Methods for Solving ?42u+A?4ut+But+C?4u+Du = 0
Mathematische Nachrichten, vol. 80, no. 1, pp. 105–113, 1977 - Hilbert function modules with reproducing kernels
Nonlinear Analysis, vol. 1, no. 2, pp. 135–150, 1977 - Hypercomplex Function Theory in the Sense of L. BERS
Mathematische Nachrichten, vol. 72, no. 1, pp. 187–200, 1976 - 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 - A Function Theoretic Method for ?32u +Q(x)u = 0
Mathematische Nachrichten, vol. 67, no. 10-14, pp. 199–212, 1975 - 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 - Generalized Hypercomplex Function Theory
Transactions of the American Mathematical Society, vol. 195, p. 1, 1974 - Corrigendum
Archive for Rational Mechanics and Analysis, vol. 48, no. 5, pp. 397–397, 1972 - 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 - 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 - SIAM Journal on Mathematical Analysis, vol. 2, no. 1, Article ID 0502002, 1971
- SIAM Journal on Mathematical Analysis, vol. 2, no. 1, Article ID 0502011, 1971
- SIAM Journal on Mathematical Analysis, vol. 1, no. 1, Article ID 0501010, 1970
- A Contribution to the Vekua-Rellich Theory of Metaharmonic Functions
American Journal of Mathematics, vol. 92, no. 3, p. 525, 1970 - SIAM Journal on Applied Mathematics, vol. 16, no. 1, Article ID 0116002, 1968
- Representation Functions of the Group of Motions of Clifford Space
Journal of Mathematical Physics, vol. 8, no. 1, p. 135, 1967 - Role of the Integral-Operator Method in the Theory of Potential Scattering
Journal of Mathematical Physics, vol. 8, no. 1, p. 141, 1967 - A New Method in the Theory of Potential Scattering
Journal of Mathematical Physics, vol. 7, no. 3, p. 431, 1966 - 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 - 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 - Analytic Properties of the Elastic Unitarity Integral
Journal of Mathematical Physics, vol. 6, no. 11, p. 1626, 1965 - Bergman's Integral Operator Method in Generalized Axially Symmetric Potential Theory
Journal of Mathematical Physics, vol. 5, no. 7, p. 983, 1964 - 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 - 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 - A Note on the Singularities of Harmonic Functions in Three Variables
Proceedings of the American Mathematical Society, vol. 13, no. 2, p. 229, 1962 - Some Properties of Generalized Axially Symmetric Potentials
American Journal of Mathematics, vol. 84, no. 3, p. 475, 1962 - On the theory of hot-water drives
Zeitschrift für angewandte Mathematik und Physik ZAMP, vol. 12, no. 6, pp. 489–496, 1961 - 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 - On a two-dimensional free-boundary problem
Zeitschrift für angewandte Mathematik und Physik ZAMP, vol. 11, no. 5, pp. 341–355, 1960 - Reversein situ combustion
Zeitschrift für angewandte Mathematik und Physik ZAMP, vol. 10, no. 6, pp. 544–551, 1959