Allaire, Grégoire (ed.); Amaziane, Brahim (ed.); Gilbert, Robert (ed.); Jäger, Willy (ed.); Piatnitski, Andrey (ed.); Vernescu, Bogdan (ed.) Introduction to the Andro Mikelic memorial volume. (English) Zbl 1493.00047 Appl. Anal. 101, No. 12, 4043-4045 (2022). MSC: 00B30 35-06 76-06 00B15 01A70 PDFBibTeX XMLCite \textit{G. Allaire} (ed.) et al., Appl. Anal. 101, No. 12, 4043--4045 (2022; Zbl 1493.00047) Full Text: DOI
Chen, Hua; Gilbert, Robert P.; Guyenne, Philippe Dispersion and attenuation in a porous viscoelastic model for gravity waves on an ice-covered ocean. (English) Zbl 1476.76009 Eur. J. Mech., B, Fluids 78, 88-105 (2019). MSC: 76B15 76S05 74F10 76-10 86A05 86A40 PDFBibTeX XMLCite \textit{H. Chen} et al., Eur. J. Mech., B, Fluids 78, 88--105 (2019; Zbl 1476.76009) Full Text: DOI
Chen, Hua; Gilbert, Robert P.; Guyenne, Philippe A Biot model for the determination of material parameters of cancellous bone from acoustic measurements. (English) Zbl 1442.92077 Inverse Probl. 34, No. 8, Article ID 085009, 28 p. (2018). MSC: 92C55 PDFBibTeX XMLCite \textit{H. Chen} et al., Inverse Probl. 34, No. 8, Article ID 085009, 28 p. (2018; Zbl 1442.92077) Full Text: DOI
Gilbert, Robert P.; Hsiao, George C.; Shoushani, Michael The Biot model for anisotropic poro-elastic media. (English) Zbl 07775155 ZAMM, Z. Angew. Math. Mech. 97, No. 2, 130-143 (2017). MSC: 35Jxx 74Fxx 74Sxx PDFBibTeX XMLCite \textit{R. P. Gilbert} et al., ZAMM, Z. Angew. Math. Mech. 97, No. 2, 130--143 (2017; Zbl 07775155) Full Text: DOI
Gilbert, Robert P.; Hsiao, George C.; Xu, Liwei On the variational formulation of a transmission problem for the Biot equations. (English) Zbl 1188.35050 Appl. Anal. 89, No. 5, 745-755 (2010). MSC: 35J05 35J20 35C15 65N38 PDFBibTeX XMLCite \textit{R. P. Gilbert} et al., Appl. Anal. 89, No. 5, 745--755 (2010; Zbl 1188.35050) Full Text: DOI
Xu, Yongzhi; Gilbert, Robert Some inverse problems raised from a mathematical model of ductal carcinoma in situ. (English) Zbl 1165.65388 Math. Comput. Modelling 49, No. 3-4, 814-828 (2009). MSC: 65M32 92C50 PDFBibTeX XMLCite \textit{Y. Xu} and \textit{R. Gilbert}, Math. Comput. Modelling 49, No. 3--4, 814--828 (2009; Zbl 1165.65388) Full Text: DOI
Gilbert, Robert; Hackl, Klaus; Xu, Yongzhi Inverse problem for wave propagation in a perturbed layered half-space. (English) Zbl 1130.74024 Math. Comput. Modelling 45, No. 1-2, 21-33 (2007). MSC: 74J25 74J20 74H25 86A22 86A15 PDFBibTeX XMLCite \textit{R. Gilbert} et al., Math. Comput. Modelling 45, No. 1--2, 21--33 (2007; Zbl 1130.74024) Full Text: DOI
Lee, Doo-Sung; Gilbert, R. P.; Zeev, Noam Classification of objects in an acoustic waveguide by inversion of the farfield data. (English) Zbl 1198.76135 J. Comput. Acoust. 14, No. 2, 185-199 (2006). MSC: 76Q05 PDFBibTeX XMLCite \textit{D.-S. Lee} et al., J. Comput. Acoust. 14, No. 2, 185--199 (2006; Zbl 1198.76135) Full Text: DOI
Lin, Zhongyan; Gilbert, R. P. Numerical algorithm based on transmutation for solving inverse wave equation. (English) Zbl 1063.65101 Math. Comput. Modelling 39, No. 13, 1467-1476 (2004). MSC: 65M32 65M70 65M12 35L05 35R30 PDFBibTeX XMLCite \textit{Z. Lin} and \textit{R. P. Gilbert}, Math. Comput. Modelling 39, No. 13, 1467--1476 (2004; Zbl 1063.65101) Full Text: DOI
Gilbert, R. P.; Vashakmadze, T. S. A two-dimensional nonlinear theory of anisotropic plates. (English) Zbl 0992.74047 Math. Comput. Modelling 32, No. 7-8, 855-875 (2000). MSC: 74K20 74E10 PDFBibTeX XMLCite \textit{R. P. Gilbert} and \textit{T. S. Vashakmadze}, Math. Comput. Modelling 32, No. 7--8, 855--875 (2000; Zbl 0992.74047) Full Text: DOI
Gilbert, R. P.; Mikelić, A. Homogenizing the acoustic properties of the seabed. I. (English) Zbl 0958.35108 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 40, No. 1-8, 185-212 (2000). Reviewer: Alexander A.Kovalevsky (Donetsk) MSC: 35Q35 76Q05 35B27 PDFBibTeX XMLCite \textit{R. P. Gilbert} and \textit{A. Mikelić}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 40, No. 1--8, 185--212 (2000; Zbl 0958.35108) Full Text: DOI
Buchanan, James L.; Gilbert, R. P.; Wirgin, A.; Xu, Yongzhi S. The unidentified object problem in a shallow ocean with a fluid-like sediment layer overlying a rigid seabed. (English) Zbl 1034.35149 Appl. Anal. 73, No. 1-2, 5-17 (1999). MSC: 35R30 65N21 86A22 PDFBibTeX XMLCite \textit{J. L. Buchanan} et al., Appl. Anal. 73, No. 1--2, 5--17 (1999; Zbl 1034.35149) Full Text: DOI
Buchanan, J. L.; Gilbert, R. P.; Wirgin, A. Finding an inclusion in a shallow ocean using the ICBA method. (English) Zbl 1054.35520 Appl. Anal. 71, No. 1-4, 347-378 (1999). MSC: 35R30 35J05 76Q05 86A05 PDFBibTeX XMLCite \textit{J. L. Buchanan} et al., Appl. Anal. 71, No. 1--4, 347--378 (1999; Zbl 1054.35520) Full Text: DOI
Gilbert, R. P.; Lin, Zhongyan; Buchanan, J. L. Direct and inverse problems in ocean acoustics. (English) Zbl 0888.35134 Nonlinear Anal., Theory Methods Appl. 30, No. 3, 1535-1546 (1997). MSC: 35R30 86A22 86A05 PDFBibTeX XMLCite \textit{R. P. Gilbert} et al., Nonlinear Anal., Theory Methods Appl. 30, No. 3, 1535--1546 (1997; Zbl 0888.35134) Full Text: DOI
Buchanan, J. L.; Gilbert, R. P. Transmission loss in the far field over a one-layer seabed assuming the Biot sediment model. (English) Zbl 0882.76089 Z. Angew. Math. Mech. 77, No. 2, 121-135 (1997). MSC: 76S05 74F10 PDFBibTeX XMLCite \textit{J. L. Buchanan} and \textit{R. P. Gilbert}, Z. Angew. Math. Mech. 77, No. 2, 121--135 (1997; Zbl 0882.76089) Full Text: DOI
Gilbert, R. P.; Xu, Yongzhi Acoustic waves and far-field patterns in two dimensional oceans with porous-elastic seabeds. (English) Zbl 0761.76092 Result. Math. 22, No. 3-4, 685-700 (1992). MSC: 76Q05 35P25 74F10 76S05 86A05 PDFBibTeX XMLCite \textit{R. P. Gilbert} and \textit{Y. Xu}, Result. Math. 22, No. 3--4, 685--700 (1992; Zbl 0761.76092) Full Text: DOI
Begehr, H.; Gilbert, R. P.; Lo, C. Y. The two-dimensional nonlinear orthotropic plate. (English) Zbl 0764.73041 J. Elasticity 26, No. 2, 147-167 (1991). Reviewer: O.John (Praha) MSC: 74K20 74B20 PDFBibTeX XMLCite \textit{H. Begehr} et al., J. Elasticity 26, No. 2, 147--167 (1991; Zbl 0764.73041) Full Text: DOI
Gilbert, Robert P.; Xu, Yongzhi Starting fields and far fields in ocean acoustics. (English) Zbl 0850.76653 Wave Motion 11, No. 6, 507-524 (1989). MSC: 76Q05 86A05 PDFBibTeX XMLCite \textit{R. P. Gilbert} and \textit{Y. Xu}, Wave Motion 11, No. 6, 507--524 (1989; Zbl 0850.76653) Full Text: DOI
Gilbert, Robert P.; Xu, Yongzhi; Wood, David H. Construction of approximations to acoustic Green’s functions for nonhomogeneous oceans using transmutation. (English) Zbl 0638.76095 Wave Motion 10, No. 3, 285-297 (1988). MSC: 76Q05 35J05 PDFBibTeX XMLCite \textit{R. P. Gilbert} et al., Wave Motion 10, No. 3, 285--297 (1988; Zbl 0638.76095) Full Text: DOI
Gilbert, R. P.; Magnanini, R. The boundary integral method for two-dimensional orthotropic materials. (English) Zbl 0618.73089 J. Elasticity 18, 61-82 (1987). Reviewer: N.F.F.Ebecken MSC: 74S30 65R20 74E10 74K20 45E99 PDFBibTeX XMLCite \textit{R. P. Gilbert} and \textit{R. Magnanini}, J. Elasticity 18, 61--82 (1987; Zbl 0618.73089) Full Text: DOI
Gilbert, Robert P.; Wood, David H. A transmutation approach to underwater sound propagation. (English) Zbl 0625.76088 Wave Motion 8, 383-397 (1986). MSC: 76Q05 35J05 65Z05 76M99 76-04 PDFBibTeX XMLCite \textit{R. P. Gilbert} and \textit{D. H. Wood}, Wave Motion 8, 383--397 (1986; Zbl 0625.76088) Full Text: DOI
Gilbert, R. P.; Schneider, M. The two-dimensional, linear, orthotropic plate: The traction problem. (English) Zbl 0614.73055 Math. Methods Appl. Sci. 8, 102-116 (1986). Reviewer: W.Velte MSC: 74K20 74S30 74E10 PDFBibTeX XMLCite \textit{R. P. Gilbert} and \textit{M. Schneider}, Math. Methods Appl. Sci. 8, 102--116 (1986; Zbl 0614.73055) Full Text: DOI
Gilbert, R. P.; Schneider, M. A bounday-layer theory for the orthotropic plate. (English) Zbl 0521.73046 Z. Angew. Math. Mech. 63, 229-237 (1983). MSC: 74K20 74E10 PDFBibTeX XMLCite \textit{R. P. Gilbert} and \textit{M. Schneider}, Z. Angew. Math. Mech. 63, 229--237 (1983; Zbl 0521.73046) Full Text: DOI
Buchanan, J.; Gilbert, R. P. The Hilbert problem for hyperanalytic functions. (English) Zbl 0462.30038 Appl. Anal. 11, 303-323 (1981). MSC: 30G35 30E25 35J67 35J55 PDFBibTeX XMLCite \textit{J. Buchanan} and \textit{R. P. Gilbert}, Appl. Anal. 11, 303--323 (1981; Zbl 0462.30038) Full Text: DOI
Gilbert, R. P.; Schneider, M. On a class of boundary value problems for a composite system of first order differential equations. (English) Zbl 0434.34011 J. Approximation Theory 25, 105-119 (1979). MSC: 34B05 PDFBibTeX XMLCite \textit{R. P. Gilbert} and \textit{M. Schneider}, J. Approx. Theory 25, 105--119 (1979; Zbl 0434.34011) Full Text: DOI
Begehr, Heinrich; Gilbert, Robert P. On Riemann boundary value problems for cerrtain linear elliptic systems in the plane. (English) Zbl 0424.35041 J. Differ. Equations 32, 1-14 (1979). MSC: 35J55 35C15 PDFBibTeX XMLCite \textit{H. Begehr} and \textit{R. P. Gilbert}, J. Differ. Equations 32, 1--14 (1979; Zbl 0424.35041) Full Text: DOI
Begehr, Heinrich; Gilbert, Robert P. Piecewise continuous solutions of pseudoparabolic equations in two space dimensions. (English) Zbl 0395.35047 Proc. R. Soc. Edinb., Sect. A 81, 153-173 (1978). MSC: 35K70 35C15 PDFBibTeX XMLCite \textit{H. Begehr} and \textit{R. P. Gilbert}, Proc. R. Soc. Edinb., Sect. A, Math. 81, 153--173 (1978; Zbl 0395.35047) Full Text: DOI
Gilbert, R. P.; Weinacht, R. J. Reproducing kernels for elliptic systems. (English) Zbl 0314.35035 J. Approximation Theory 15, 243-255 (1975). MSC: 35J55 35P10 65N99 65M99 35B20 35C15 PDFBibTeX XMLCite \textit{R. P. Gilbert} and \textit{R. J. Weinacht}, J. Approx. Theory 15, 243--255 (1975; Zbl 0314.35035) Full Text: DOI
Gilbert, R. P.; Kukral, D. A function theoretic method for \(\Delta^2_4u+Q(x)u=0\). (English) Zbl 0303.35033 Ann. Mat. Pura Appl., IV. Ser. 104, 31-42 (1975). MSC: 35J30 35C10 PDFBibTeX XMLCite \textit{R. P. Gilbert} and \textit{D. Kukral}, Ann. Mat. Pura Appl. (4) 104, 31--42 (1975; Zbl 0303.35033) Full Text: DOI
Conlan, James; Gilbert, Robert P. Initial value problems for fourth order, semi-linear elliptic equations. (English) Zbl 0298.35023 Appl. Analysis 3, 321-331 (1974). MSC: 35J60 35A05 PDFBibTeX XMLCite \textit{J. Conlan} and \textit{R. P. Gilbert}, Appl. Anal. 3, 321--331 (1974; Zbl 0298.35023) Full Text: DOI
Gilbert, R. P.; Kukral, D. Function theoretic methods for higher order, elliptic equations in three independent variables. (English) Zbl 0259.35028 Bull. Am. Math. Soc. 79, 96-99 (1973). MSC: 35A20 35C15 35J30 PDFBibTeX XMLCite \textit{R. P. Gilbert} and \textit{D. Kukral}, Bull. Am. Math. Soc. 79, 96--99 (1973; Zbl 0259.35028) Full Text: DOI
Colton, David; Gilbert, R. P. Integral operators and complete families of solutions for \(\Delta^ 2_{p+2}u(x) + A(r^ 2)\Delta_{p+2}u(x) + B(r^ 2)u(x) = 0\). (English) Zbl 0225.35018 Arch. Ration. Mech. Anal. 43, 62-78 (1971). MSC: 35C15 PDFBibTeX XMLCite \textit{D. Colton} and \textit{R. P. Gilbert}, Arch. Ration. Mech. Anal. 43, 62--78 (1971; Zbl 0225.35018) Full Text: DOI