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Functional Analysis and Sobolev Spaces Read chapter Read first chapter

2014 | OriginalPaper | Chapter

5. Scattering by Orthotropic Media

Authors : Fioralba Cakoni, David Colton

Published in: A Qualitative Approach to Inverse Scattering Theory

Publisher: Springer US

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Abstract

Until now the reader has been introduced only to the scattering of time-harmonic electromagnetic waves by an imperfect conductor. We will now consider the scattering of electromagnetic waves by a penetrable orthotropic inhomogeneity embedded in a homogeneous background. As in the previous chapter, we will confine ourselves to the scalar case that corresponds to the scattering of electromagnetic waves by an orthotropic infinite cylinder. The direct scattering problem is now modeled by a transmission problem for the Helmholtz equation outside the scatterer and an equation with nonconstant coefficients inside the scatterer. This chapter is devoted to the analysis of the solution to the direct problem.

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previous chapter Inverse Scattering Problems for Imperfect Conductors
next chapter Inverse Scattering Problems for Orthotropic Media
Literature
1.
Aktosun T, Gintides D, Papanicolaou V (2011) The uniqueness in the inverse problem for transmission eigenvalues for the spherically symmetric variable-speed wave equation. Inverse Problems 27:115004.MathSciNet
2.
Aktosun T, Papanicolaou V (2013) Reconstruction of the wave speed from transmission eigenvalues for the spherically symmetric variable-speed wave equation. Inverse Problems 29:065007.MathSciNet
3.
Angell T, Kirsch A (1992) The conductive boundary condition for Maxwell’s equations. SIAM J. Appl. Math. 52:1597–1610.MathSciNetMATH
4.
Angell T, Kirsch A (2004) Optimization Methods in Electromagnetic Radiation. Springer, New York.MATH
5.
Arens T (2001) Linear sampling methods for 2D inverse elastic wave scattering. Inverse Problems 17:1445–1464.MathSciNetMATH
6.
7.
Arens T, Lechleiter A(2009) The linear sampling method revisited. J. Integral Equations Appl. 21:179–203.MathSciNetMATH
8.
Boas Jr, Ralph P (1954) Entire Functions. Academic, New York.
9.
Bonnet-BenDhia AS, Chesnel L, Haddar H (2011) On the use of t-coercivity to study the interior transmission eigenvalue problem. C. R. Acad. Sci., Ser. I 340:647–651.MathSciNet
10.
Bonnet-BenDhia AS, Ciarlet P, Maria Zwölf C (2010) Time harmonic wave diffraction problems in materials with sign-shifting coefficients. J. Comput. Appl. Math 234:1912–1919.MathSciNet
11.
Bressan A (2013) Lecture Notes on Functional Analysis with Applications to Linear Partial Differential Equations. American Mathematical Society, Providence, RI.MATH
12.
Buchanan JL, Gilbert RP, Wirgin A, Xu Y (2004) Marine Acoustics. Direct and Inverse Problems. SIAM, Philadelphia.MATH
13.
Cakoni F, Colton D (2003) A uniqueness theorem for an inverse electomagnetic scattering problem in inhomogeneous anisotropic media. Proc. Edinb. Math. Soc. 46:293–314.MathSciNetMATH
14.
Cakoni F, Colton D (2003) On the mathematical basis of the linear sampling method. Georgian Math. J. 10/3:411–425.
15.
16.
Cakoni F, Colton D (2003) Combined far field operators in electromagnetic inverse scattering theory. Math. Methods Appl. Sci. 26:413–429.MathSciNetMATH
17.
Cakoni F, Colton D (2004) The determination of the surface impedance of a partially coated obstacle from far field data. SIAM J. Appl. Math. 64:709–723.MathSciNetMATH
18.
Cakoni F, Colton D (2005) Open problems in the qualitative approach to inverse electromagnetic scattering theory. Eur. J. Appl. Math. to appear.
19.
Cakoni F, Colton D, Gintides D (2010) The interior transmission eigenvalue problem. SIAM J. Math. Anal. 42:2912–2921.MathSciNetMATH
20.
Cakoni F, Colton D, Haddar H (2002) The linear sampling method for anisotropic media. J. Comp. Appl. Math. 146:285–299.MathSciNetMATH
21.
Cakoni F, Colton D, Haddar H (2009) The computation of lower bounds for the norm of the index of refraction in an anisotropic media. J. Integral Equations Appl. 21(2):203–227.MathSciNetMATH
22.
Cakoni F, Colton D, Haddar H (2010) On the determination of Dirichlet or transmission eigenvalues from far field data. C. R. Math. Acad. Sci. Paris, Ser I 348(7–8):379–383.MathSciNetMATH
23.
Cakoni F, Colton D, Monk P (2001) The direct and inverse scattering problems for partially coated obstacles. Inverse Problems 17:1997–2015.MathSciNetMATH
24.
Cakoni F, Colton D, Monk P (2004) The electromagnetic inverse scattering problem for partly coated Lipschitz domains. Proc. R. Soc. Edinb. 134A:661–682.MathSciNet
25.
Cakoni F, Colton D, Monk P (2010) The determination of boundary coefficients from far field measurements. J. Int. Equations Appl. 42(2):167–191.MathSciNet
26.
Cakoni F, Colton D, Monk P (2011) The Linear Sampling Method in Inverse Electromagnetic Scattering. CBMS-NSF Regional Conference Series in Applied Mathematics 80, SIAM, Philadelphia.
27.
Cakoni F, Colton D, Monk P (2005) The determination of the surface conductivity of a partially coated dielectric. SIAM J. Appl. Math. 65:767–789.MathSciNetMATH
28.
Cakoni F, Colton D, Monk P, Sun J (2010) The inverse electromagnetic scattering problem for anisotropic media. Inverse Problems 26:074004.MathSciNet
29.
Cakoni F, Darrigrand E (2005) The inverse electromagnetic scattering problem for a mixed boundary value problem for screens. J. Comp. Appl. Math. 174:251–269.MathSciNetMATH
30.
Cakoni F, Fares M, Haddar H (2006) Anals of two linear sampling methods applied to electromagnetic imaging of buried objects. Inverse Problems 42:237–255.MathSciNet
31.
Cakoni F, Gintides D, Haddar H (2010) The existence of an infinite discrete set of transmission eigenvalues. SIAM J. Math. Anal. 42:237–255.MathSciNetMATH
32.
Cakoni F, Haddar H (2013) Transmission eigenvalues in inverse scattering theory Inverse Problems and Applications, Inside Out 60, MSRI Publications, Berkeley, CA.
33.
Cakoni F, Haddar H (2008), On the existence of transmission eigenvalues in an inhomogeneous medium. Applicable Anal. 88(4):475–493.MathSciNet
34.
Cakoni F, Haddar H (2003) Interior transmission problem for anisotropic media. Mathematical and Numerical Aspects of Wave Propagation (Cohen et al., eds.), Springer, 613–618.
35.
Cakoni F, Kirsch A (2010) On the interior transmission eigenvalue problem (2010) Int. J. Comp. Sci. Math. 3:142–167.MathSciNetMATH
36.
Chanillo S, Helffer B, Laptev A (2004) Nonlinear eigenvalues and analytic hypoellipticity. J. Functional Analysis 209:425–443.MathSciNetMATH
37.
Charalambopoulos A, Gintides D, Kiriaki K (2002) The linear sampling method for the transmission problem in three-dimensional linear elasticity. Inverse Problems 18:547–558.MathSciNetMATH
38.
Charalambopoulos A, Gintides D, Kiriaki K (2003) The linear sampling method for non-absorbing penetrable elastic bodies. Inverse Problems 19:549–561.MathSciNetMATH
39.
Chesnel L (2012) Étude de quelques problémes de transmission avec changement de signe. Application aux métamatériaux. Ph.D. thesis. École Doctorale de l’École Polytechnique, France.
40.
Chesnel L (2012) Interior transmission eigenvalue problem for Maxwell’s equations: the T-coercivity as an alternative approach. Inverse Problems 28:065005.MathSciNet
41.
Cheng J, Yamamoto M (2003) Uniqueness in an inverse scattering problem within non-trapping polygonal obstacles with at most two incoming waves. Inverse Problems 19:1361–1384.MathSciNet
42.
Collino F, Fares M, Haddar H (2003) Numerical and analytical studies of the linear sampling method in electromagnetic inverse scattering problems. Inverse Problems 19:1279–1298.MathSciNetMATH
43.
Colton D (2004) Partial Differential Equations: An Introduction. Dover, New York.
44.
Colton D, Coyle J, Monk P (2000) Recent developments in inverse acoustic scattering theory. SIAM Rev. 42:369–414.MathSciNetMATH
45.
Colton D (1980) Analytic Theory of Partial Differential Equations. Pitman Advanced Publishing Program, Boston.MATH
46.
Colton D, Erbe C (1996) Spectral theory of the magnetic far field operator in an orthotropic medium, in Nonlinear Problems in Applied Mathematics, SIAM, Philadelphia.
47.
Colton D, Haddar H (2005) An application of the reciprocity gap functional to inverse scattering theory. Inverse Problems 21:383–398.MathSciNetMATH
48.
Colton D, Haddar H, Monk P (2002) The linear sampling method for solving the electromagnetic inverse scattering problem. SIAM J. Sci. Comput. 24:719–731.MathSciNetMATH
49.
Colton D, Haddar H, Piana P (2003) The linear sampling method in inverse electromagnetic scattering theory. Inverse Problems 19:S105–S137.MathSciNetMATH
50.
Colton D, Kirsch A (1996) A simple method for solving inverse scattering problems in the resonance region. Inverse Problems 12:383–393.MathSciNetMATH
51.
Colton D, Kress R (1983) Integral Equation Methods in Scattering Theory. Wiley, New York.MATH
52.
Colton D, Kress R (1995) Eigenvalues of the far field operator and inverse scattering theory. SIAM J. Math. Anal. 26:601–615.MathSciNetMATH
53.
Colton D, Kress R (1995) Eigenvalues of the far field operator for the Helmholtz equation in an absorbing medium. SIAM J. Appl. Math. 55:1724–35.MathSciNetMATH
54.
Colton D, Kress R (2013) Inverse Acoustic and Electromagnetic Scattering Theory, 3rd edn. Springer, New York.MATH
55.
Colton D, Kress R (2001) On the denseness of Herglotz wave functions and electromagnetic Herglotz pairs in Sobolev spaces. Math. Methods Appl. Sci. 24:1289–1303.MathSciNetMATH
56.
Colton D, Leung YJ (2013) Complex eigenvalues and the inverse spectral problem for transmission eigenvalues. Inverse Problems. 29:104008.
57.
Colton D, Kress R, Monk P. (1997) Inverse scattering from an orthotropic medium. J. Comp. Appl. Math. 81:269–298.MathSciNetMATH
58.
Colton D, Monk P. (1999) A linear sampling method for the detection of leukemia using microwaves. II. SIAM J. Appl. Math. 69, 241–255.
59.
Colton D, Päivarinta L (1992) The uniqueness of a solution to an inverse scattering problem for electromagnetic wave. Arch. Rational Mech. Anal. 119:59–70.MathSciNetMATH
60.
Colton D, Päivärinta L, Sylvester J (2007) The interior transmission problem. Inverse Problems Imag. 1:13–28.MATH
61.
Colton D, Piana M, Potthast R (1997) A simple method using Morozov’s discrepancy principle for solving inverse scattering problems. Inverse Problems 13:1477–1493.MathSciNetMATH
62.
Colton D, Sleeman BD (1983) Uniqueness theorems for the inverse problem of acoustic scattering. IMA J. Appl. Math. 31:253–59.MathSciNetMATH
63.
Colton D, Sleeman BD (2001) An approximation property of importance in inverse scattering theory. Proc. Edinb. Math. Soc. 44:449–454.MathSciNetMATH
64.
Costabel M, Dauge M (2002) Crack singularities for general elliptic systems. Math. Nachr. 235:29–49.MathSciNetMATH
65.
Costabel M, Dauge M (1996) A singularly perturbed mixed boundary value problem. Comm. Partial Differential Equations 21:1919–1949.MathSciNetMATH
66.
Cossonnière A, Haddar H (2011) The electromagnetic interior transmission problem for regions with cavities. SIAM J. Math. Anal. 43:1698–1715.MathSciNetMATH
67.
Coyle J (2000) An inverse electromagnetic scattering problem in a two-layered background. Inverse Problems 16:275–292.MathSciNetMATH
68.
Engl HW, Hanke M, Neubauer A (1996) Regularization of Inverse Problems. Kluwer, Dordrecht.MATH
69.
70.
Friedman A (1969) Partial Differential Equations. Holt, Rinehart and Winston, New York.MATH
71.
Ghosh Roy DN, Couchman LS (2002) Inverse Problems and Inverse Scattering of Plane Waves. Academic, London.
72.
Gilbarg D, Trudinger NS (1983) Elliptic Partial Differential Equations of Second Order, 2nd edn. Springer, Berlin.MATH
73.
Gintides D, Kiriaki K (2001) The far-field equations in linear elasticity – an inversion scheme. Z. Angew. Math. Mech. 81:305–316.MathSciNetMATH
74.
Griesmaier R, Hanke M, Sylvester J (to appear) Far field splitting for the Helmholtz equation.
75.
Grinberg NI, Kirsch A (2002) The linear sampling method in inverse obstacle scattering for impedance boundary conditions. J. Inv. Ill-Posed Problems 10:171–185.MathSciNetMATH
76.
Grinberg NI, Kirsch A (2004) The factorization method for obstacles with a-priori separated sound-soft and sound-hard parts. Math. Comput. Simulation 66:267–279MathSciNetMATH
77.
Gylys-Colwell F (1996) An inverse problem for the Helmholtz equation. Inverse Problems 12:139–156.MathSciNetMATH
78.
Haddar H (2004) The interior transmission problem for anisotropic Maxwell’s equations and its applications to the inverse problem. Math. Methods Appl. Sci. 27:2111–2129.MathSciNetMATH
79.
Haddar H, Joly P (2002)Stability of thin layer approximation of electromagnetic waves scattering by linear and nonlinear coatings. J. Comp. Appl. Math. 143:201–236.MathSciNetMATH
80.
Haddar H, Monk P (2002) The linear sampling method for solving the electromagnetic inverse medium problem. Inverse Problems 18:891–906.MathSciNetMATH
81.
Hähner P (2000) On the uniqueness of the shape of a penetrable, anisotropic obstacle. J. Comp. Appl. Math. 116:167–180.MATH
82.
Hähner P (2002) Electromagnetic wave scattering: theory. in Scattering (Pike and Sabatier, eds.) Academic, New York.
83.
Hartman P, Wilcox C (1961) On solutions of the Helmholtz equation in exterior domains. Math. Zeit. 75:228–255.MathSciNetMATH
84.
Hitrik M, Krupchyk K, Ola P, Päivärinta L (2010) Transmission eigenvalues for operators with constant coefficients. SIAM J. Math. Anal. 42:2965–2986.MathSciNetMATH
85.
Hitrik M, Krupchyk K, Ola P and Päivärinta L (2011) The interior transmission problem and bounds on transmission eigenvalues. Math Res. Lett. 18:279–293.MathSciNetMATH
86.
Hitrik M, Krupchyk K, Ola P, Päivärinta L (2011) Transmission eigenvalues for elliptic operators. SIAM J. Math. Anal. 43:2630–2639.MathSciNetMATH
87.
88.
Hooper AE, Hambric HN (1999) Unexploded ordinance (UXO): The problem. Detection and Identification of Visually Obscured Targets (Baum, ed.), Taylor and Francis, Philadelphia.
89.
Hörmander L (1985) The Analysis of Linear Partial Differential Operators III. Springer, Berlin.MATH
90.
Hsiao G, Wendland WL (2008) Boundary Integral Equations. Springer, Berlin.MATH
91.
Ikehata M (1998) Reconstruction of the shape of an obstacle from scattering amplitude at a fixed frequency. Inverse Problems 14:949–954.MathSciNetMATH
92.
Ikehata M (1999) Reconstructions of obstacle from boundary measurements. Waves Motion 30:205–223.MathSciNetMATH
93.
Isakov V (1988) On the uniqueness in the inverse transmission scattering problem. Comm. Partial Differential Equations 15:1565–1587.MathSciNet
94.
Isakov V (1998) Inverse Problems for Partial Differential Equations. Springer, New York.MATH
95.
John F (1982) Partial Differential Equations, 4th ed. Springer Verlag, New York.MATH
96.
Jones DS (1974) Integral equations for the exterior acoustic problem. Q. J. Mech. Appl. Math. 27:129–142.MATH
97.
Y. Katznelson (9168) An Introduction to Harmonic Analysis. Wiley, New York.
98.
Kirsch A (2011) An Introduction to the Mathematical Theory of Inverse Problems, 2nd edn. Springer, New York.MATH
99.
Kirsch A (1998) Characterization of the shape of a scattering obstacle using the spectral data of the far field operator. Inverse Problems 14:1489–1512.MathSciNetMATH
100.
Kirsch A (1999) Factorization of the far field operator for the inhomogeneous medium case and an application in inverse scattering theory. Inverse Problems 15:413–29.MathSciNetMATH
101.
Kirsch A (2002) The MUSIC-algorithm and the factorization method in inverse scattering theory for inhomogeneous media. Inverse Problems 18:1025–1040.MathSciNetMATH
102.
103.
Kirsch A (2005) The factorization method for a class of inverse elliptic problems. Math. Nachr. 278:258–277.MathSciNetMATH
104.
Kirsch A (2008) An integral equation for the scattering problem for an anisotropic medium and the factorization method. Advanced Topics in Scattering and Biomedical Engineering, Proceedings of the 8th International Workshop on Mathematical Methods in Scattering Theory and Biomedical Engineering. World Scientific, New Jersey.
105.
106.
107.
Kirsch A, Grinberg N (2008) The Factorization Method for Inverse Problems. Oxford University Press, Oxford.MATH
108.
Kirsch A, Ritter S (2000) A linear sampling method for inverse scattering from an open arc. Inverse Problems 16:89–105.MathSciNetMATH
109.
Kleinman RE, Roach GF (1982) On modified Green’s functions in exterior problems for the Helmholtz equation. Proc. R. Soc. Lond. A383:313–332.MathSciNet
110.
111.
Kress R (1999) Linear Integral Equations, 2nd edn. Springer, New York.MATH
112.
Kress R, Lee KM (2003) Integral equation methods for scattering from an impedance crack. J. Comp. Appl. Math. 161:161–177.MathSciNetMATH
113.
Kress R, Rundell W (2001) Inverse scattering for shape and impedance. Inverse Problems 17:1075–1085.MathSciNetMATH
114.
Kress R, Serranho P (2005) A hybrid method for two-dimensional crack reconstruction. Inverse Problems 21:773–784.MathSciNetMATH
115.
Kreyszig E (1978) Introductory Functional Analysis with Applications. Wiley, New York.MATH
116.
117.
Kusiak S, Sylvester J (2005) The convex scattering support in a background medium. SIAM J. Math. Anal. 36:1142–1158.MathSciNetMATH
118.
Lakshtanov E, Vainberg B (2012) Bounds on positive interior transmission eigenvalues. Inverse Problems 28:105005.MathSciNet
119.
Lakshtanov E, Vainberg B (2012) Remarks on interior transmission eigenvalues, Weyl formula and branching billiards. J. Phys. A 25 12:125202.
120.
Lakshtanov E, Vainberg B (2012) Ellipticity in the interior transmission problem in anisotropic media. SIAM J. Math. Anal. 44 2:1165–1174.MathSciNetMATH
121.
Lebedev NN (1965) Special Functions and Their Applications. Prentice-Hall, Englewood Cliffs, NJ.MATH
122.
Leung YJ, Colton D (2012) Complex transmission eigenvalues for spherically stratified media. Inverse Problems 28:2944956.MathSciNet
123.
Levin B Y (1996) Lectures on Entire Functions. American Mathematical Society. Providence, RI.MATH
124.
Lions J, Magenes E (1972) Non-homogeneous Boundary Value Problems and Applications. Springer, New York.
125.
Magnus W (1949) Fragen der Eindeutigkeit und des Verhattens im Unendlichen für Lösungen von Δ u + k 2 u = 0. Abh. Math. Sem. Hamburg 16:77–94.MathSciNetMATH
126.
McLaughlin JR, Polyakov PL (1994) On the uniqueness of a spherically symmetric speed of sound from transmission eigenvalues. J. Differential Equations 107:351–382.MathSciNetMATH
127.
McLean W (2000) Strongly Elliptic Systems and Boundary Integral Equations. Cambridge University Press, Cambridge.MATH
128.
Mönch L (1997) On the inverse acoustic scattering problem by an open arc: the sound-hard case. Inverse Problems 13:1379–1392MathSciNetMATH
129.
Monk P (2003) Finite Element Methods for Maxwell’s Equations. Oxford University Press, Oxford.MATH
130.
Morozov VA (1984) Methods for Solving Incorrectly Posed Problems. Springer, New York.
131.
Müller C (1952) Über die ganzen Lösungen der Wellengleichung. Math. Annalen 124:235–264MATH
132.
Nintcheu Fata S, Guzina BB (2004) A linear sampling method for near-field inverse problems in elastodynamics. Inverse Problems 20:713–736.MathSciNetMATH
133.
Norris AN (1998) A direct inverse scattering method for imaging obstacles with unknown surface conditions. IMA J. Applied Math. 61:267–290.MathSciNetMATH
134.
Päivärinta L, Sylvester J. (2008) Transmission eigenvalues. SIAM J. Math. Anal. 40 738–753.
135.
Pelekanos G, Sevroglou V (2003) Inverse scattering by penetrable objects in two-dimensional elastodynamics. J. Comp. Appl. Math. 151:129–140.MathSciNetMATH
136.
Piana M (1998) On uniqueness for anisotropic inhomogeneous inverse scattering problems. Inverse Problems 14:1565–1579.MathSciNetMATH
137.
Potthast R (1999) Electromagnetic scattering from an orthotropic medium. J. Integral Equations Appl. 11:197–215.MathSciNetMATH
138.
Potthast R (2000) Stability estimates and reconstructions in inverse acoustic scattering using singular sources. J. Comp. Appl. Math. 114:247–274.MathSciNetMATH
139.
Potthast R (2001) Point Sourse and Multipoles in Inverse Scattering Theory. Research Notes in Mathematics, Vol 427, Chapman and Hall/CRC, Boca Raton, FL.
140.
Potthast R (2004) A new non-iterative singular sources method for the reconstruction of piecewise constant media. Numer. Math. 98:703–730.MathSciNetMATH
141.
Potthast R, Sylvester J, Kusiak S (2003) A ’range test’ for determining scatterers with unknown physical properties. Inverse Problems 19:533–47.MathSciNetMATH
142.
Pöschel J, Trubowitz E (1987) Inverse Spectral Theory. Academic, Boston.MATH
143.
Rellich F (1943) Über das asymptotische Verhalten der Lösungen von △ u +λ u = 0 im unendlichen Gebieten. Jber. Deutsch. Math. Verein. 53:57–65.MathSciNetMATH
144.
145.
146.
Rondi L (2003) Unique determination of non-smooth sound-soft scatteres by finitely many far field measurements. Indiana University Math. J. 52:1631–62.MathSciNetMATH
147.
Rundell W, Sacks P (1992) Reconstruction techniques for classical inverse Sturm-Liouville problems. Math. Comput. 58:161–183.MathSciNetMATH
148.
Rynne BP, Sleeman BD (1991) The interior transmission problem and inverse scattering from inhomogeneous media. SIAM J. Math. Anal. 22:1755–1762.MathSciNetMATH
149.
Schechter M (2002) Principles of Functional Analysis, 2nd edn. American Mathematical Society, Providence, RI.
150.
Sevroglou V (2005) The far-field operator for penetrable and absorbing obstacles in 2D inverse elastic scattering. Inverse Problems 21:717–738.MathSciNetMATH
151.
Stefanov P, Uhlmann G (2004) Local uniqueness for the fixed energy fixed angle inverse problem in obstacle scattering. Proc. Am. Math. Soc. 132:1351–54.MathSciNetMATH
152.
Stephan EP (1987) Boundary integral equations for screen problems in ℝ 3. Integral Equations Operator Theory 10:236–257.MathSciNetMATH
153.
Stephan EP, Wendland W (1984) An augmented Galerkin procedure for the boundary integral method applied to two-dimensional screen and crack problems. Appl. Anal. 18:183–219.MathSciNet
154.
Sylvester J (2012) Discreteness of transmission eigenvalues via upper triangular compact operator. SIAM J. Math. Anal. 44:341–354.MathSciNetMATH
155.
Tacchino A, Coyle J, Piana M (2002) Numerical validation of the linear sampling method. Inverse Problems 18:511–527.MathSciNetMATH
156.
157.
Vekua IN (1943) Metaharmonic functions. Trudy Tbilisskogo Matematichesgo Instituta 12:105–174.
158.
Xu Y, Mawata C, Lin W (2000) Generalized dual space indicator method for underwater imaging. Inverse Problems 16:1761–1776.MathSciNetMATH
159.
You YX, Miao GP (2002) An indicator sampling method for solving the inverse acoustic scattering problem from penetrable obstacles. Inverse Problems 18:859–880.MathSciNetMATH
160.
You YX, Miao GP, Liu YZ (2000) A fast method for acoustic imaging of multiple three-dimensional objects. J. Acoust. Soc. Am. 108:31–37.
161.
Young RM (2001) An Introduction to Nonharmonic Fourier Series. Academic, San Diego.MATH
Metadata
Title
Scattering by Orthotropic Media
Authors
Fioralba Cakoni
David Colton
Copyright Year
2014
Publisher
Springer US
Book
A Qualitative Approach to Inverse Scattering Theory

Print ISBN: 978-1-4614-8826-2

Electronic ISBN: 978-1-4614-8827-9

Copyright Year: 2014

DOI
https://doi.org/10.1007/978-1-4614-8827-9_5