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Factorization method in inverse interaction problems with bi-periodic interfaces between acoustic and elastic waves
The enclosure method for inverse obstacle scattering using a single electromagnetic wave in time domain
1. | Laboratory of Mathematics, Institute of Engineering, Hiroshima University, Higashi Hiroshima 739-8527 |
References:
[1] |
H. Ammari, G. Bao and J. L. Fleming, An inverse source problem for Maxwell's equations in magnetoencephalography, SIAM J. Appl. Math., 62 (2002), 1369-1382.
doi: 10.1137/S0036139900373927. |
[2] |
H. Ammari, C. Latiri-Grouz and J.-C. Nédélec, The Leontovich boundary value problem for the time-harmonic Maxwell equations, Asymptotic Analysis, 18 (1998), 33-47. |
[3] |
C. Athanasiadis, P. A. Martin and I. G. Stratis, On the scattering of point-generated electromagnetic waves by a perfectly conducting sphere, and related near-field inverse problems, Short Communication, ZAMM$\cdot$Z. Angew. Math. Mech. 83 (2003), 129-136.
doi: 10.1002/zamm.200310012. |
[4] |
C. A. Balanis, Antenna Theory, Analysis and Design, $3^{rd}$ edition, Wiley-Interscience, Hoboken, New Jersey, 2005. |
[5] |
N. Bleistein and R. A. Handelsman, Asymptotic Expansions of Integrals, $2^{nd}$ edition, Dover Publications, New York, 1986. |
[6] |
R. J. Burkholder, I. J. Gupta and J. T. Johnson, Comparison of monostatic and bistatic radar images, IEEE Antennas and Propagation Magazine, 45 (2003), 41-50. |
[7] |
M. Cheney and B. Borden, Fundamentals of Radar Imaging, CBMS-NSF, Regional Conference Series in Applied Mathematics, 79, SIAM, Philadelphia, 2009.
doi: 10.1137/1.9780898719291. |
[8] |
D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, $3^{rd}$ edition, New York, Springer, 2013.
doi: 10.1007/978-1-4614-4942-3. |
[9] |
R. Courant and D. Hilbert, Methoden der Mathematischen Physik, Vol. 2, Berlin, Springer, 1937. |
[10] |
R. Dautray and J.-L. Lions., Mathematical Analysis and Numerical Methods for Sciences and Technology, Spectral Theory and Applications, Vol. 3, Springer-Verlag, Berlin, 1990. |
[11] |
R. Dautray and J.-L. Lions, Mathematical Analysis and Numerical Methods for Sciences and Technology, Vol. 5, Evolution Problems I, Springer-Verlag, Berlin, 1992.
doi: 10.1007/978-3-642-58090-1. |
[12] |
D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Reprint of the 1998 ed., Springer-Verlag, Berlin, Heidelberg, New York, 2001. |
[13] |
M. Ikehata, Enclosing a polygonal cavity in a two-dimensional bounded domain from Cauchy data, Inverse Problems, 15 (1999), 1231-1241.
doi: 10.1088/0266-5611/15/5/308. |
[14] |
M. Ikehata, The enclosure method for inverse obstacle scattering problems with dynamical data over a finite time interval, Inverse Problems, 26 (2010), 055010, 20pp.
doi: 10.1088/0266-5611/26/5/055010. |
[15] |
M. Ikehata, The enclosure method for inverse obstacle scattering problems with dynamical data over a finite time interval: II. Obstacles with a dissipative boundary or finite refractive index and back-scattering data, Inverse Problems, 28 (2012), 045010, 29pp.
doi: 10.1088/0266-5611/28/4/045010. |
[16] |
M. Ikehata, An inverse acoustic scattering problem inside a cavity with dynamical back-scattering data, Inverse Problems, 28 (2012), 095016, 24pp.
doi: 10.1088/0266-5611/28/9/095016. |
[17] |
M. Ikehata, The enclosure method for inverse obstacle scattering problems with dynamical data over a finite time interval: III. Sound-soft obstacle and bistatic data, Inverse Problems, 29 (2013), 085013, 35pp.
doi: 10.1088/0266-5611/29/8/085013. |
[18] |
M. Ikehata, Extracting the geometry of an obstacle and a zeroth-order coefficient of a boundary condition via the enclosure method using a single reflected wave over a finite time interval, Inverse Problems, 30 (2014), 045011, 24pp.
doi: 10.1088/0266-5611/30/4/045011. |
[19] |
M. Ikehata and H. Itou, On reconstruction of a cavity in a linearized viscoelastic body from infinitely many transient boundary data, Inverse Problems, 28 (2012), 125003, 19pp.
doi: 10.1088/0266-5611/28/12/125003. |
[20] |
M. Ikehata and M. Kawashita, On the reconstruction of inclusions in a heat conductive body from dynamical boundary data over a finite time interval, Inverse Problems, 26 (2010), 095004, 15pp.
doi: 10.1088/0266-5611/26/9/095004. |
[21] |
V. Isakov, Inverse obstacle problems, Topical review, Inverse Problems, 25 (2009), 123002, 18pp.
doi: 10.1088/0266-5611/25/12/123002. |
[22] |
P. D. Lax and R. S. Phillips, The scattering of sound waves by an obstacle, Comm. Pure and Appl. Math., 30 (1977), 195-233.
doi: 10.1002/cpa.3160300204. |
[23] |
H. Liu, M. Yamamoto and J. Zou, Reflection principle for the Maxwell equations and its application to inverse electromagnetic scattering, Inverse Problems, 23 (2007), 2357-2366.
doi: 10.1088/0266-5611/23/6/005. |
[24] |
A. Majda and M. Taylor, Inverse scattering problems for transparent obstacles, electromagnetic waves, and hyperbolic systems, Comm. in Partial Differential Equations, 2 (1977), 395-438.
doi: 10.1080/03605307708820035. |
[25] |
J.-C. Nédélec, Acoustic and Electromagnetic Equations, Integral Representations for Harmonic Problems, Springer, New York, 2001.
doi: 10.1007/978-1-4757-4393-7. |
[26] |
B. O'Neill, Elementary Differential Geometry, Revised, $2^{nd}$ edition, Academic Press, 2006. |
show all references
References:
[1] |
H. Ammari, G. Bao and J. L. Fleming, An inverse source problem for Maxwell's equations in magnetoencephalography, SIAM J. Appl. Math., 62 (2002), 1369-1382.
doi: 10.1137/S0036139900373927. |
[2] |
H. Ammari, C. Latiri-Grouz and J.-C. Nédélec, The Leontovich boundary value problem for the time-harmonic Maxwell equations, Asymptotic Analysis, 18 (1998), 33-47. |
[3] |
C. Athanasiadis, P. A. Martin and I. G. Stratis, On the scattering of point-generated electromagnetic waves by a perfectly conducting sphere, and related near-field inverse problems, Short Communication, ZAMM$\cdot$Z. Angew. Math. Mech. 83 (2003), 129-136.
doi: 10.1002/zamm.200310012. |
[4] |
C. A. Balanis, Antenna Theory, Analysis and Design, $3^{rd}$ edition, Wiley-Interscience, Hoboken, New Jersey, 2005. |
[5] |
N. Bleistein and R. A. Handelsman, Asymptotic Expansions of Integrals, $2^{nd}$ edition, Dover Publications, New York, 1986. |
[6] |
R. J. Burkholder, I. J. Gupta and J. T. Johnson, Comparison of monostatic and bistatic radar images, IEEE Antennas and Propagation Magazine, 45 (2003), 41-50. |
[7] |
M. Cheney and B. Borden, Fundamentals of Radar Imaging, CBMS-NSF, Regional Conference Series in Applied Mathematics, 79, SIAM, Philadelphia, 2009.
doi: 10.1137/1.9780898719291. |
[8] |
D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, $3^{rd}$ edition, New York, Springer, 2013.
doi: 10.1007/978-1-4614-4942-3. |
[9] |
R. Courant and D. Hilbert, Methoden der Mathematischen Physik, Vol. 2, Berlin, Springer, 1937. |
[10] |
R. Dautray and J.-L. Lions., Mathematical Analysis and Numerical Methods for Sciences and Technology, Spectral Theory and Applications, Vol. 3, Springer-Verlag, Berlin, 1990. |
[11] |
R. Dautray and J.-L. Lions, Mathematical Analysis and Numerical Methods for Sciences and Technology, Vol. 5, Evolution Problems I, Springer-Verlag, Berlin, 1992.
doi: 10.1007/978-3-642-58090-1. |
[12] |
D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Reprint of the 1998 ed., Springer-Verlag, Berlin, Heidelberg, New York, 2001. |
[13] |
M. Ikehata, Enclosing a polygonal cavity in a two-dimensional bounded domain from Cauchy data, Inverse Problems, 15 (1999), 1231-1241.
doi: 10.1088/0266-5611/15/5/308. |
[14] |
M. Ikehata, The enclosure method for inverse obstacle scattering problems with dynamical data over a finite time interval, Inverse Problems, 26 (2010), 055010, 20pp.
doi: 10.1088/0266-5611/26/5/055010. |
[15] |
M. Ikehata, The enclosure method for inverse obstacle scattering problems with dynamical data over a finite time interval: II. Obstacles with a dissipative boundary or finite refractive index and back-scattering data, Inverse Problems, 28 (2012), 045010, 29pp.
doi: 10.1088/0266-5611/28/4/045010. |
[16] |
M. Ikehata, An inverse acoustic scattering problem inside a cavity with dynamical back-scattering data, Inverse Problems, 28 (2012), 095016, 24pp.
doi: 10.1088/0266-5611/28/9/095016. |
[17] |
M. Ikehata, The enclosure method for inverse obstacle scattering problems with dynamical data over a finite time interval: III. Sound-soft obstacle and bistatic data, Inverse Problems, 29 (2013), 085013, 35pp.
doi: 10.1088/0266-5611/29/8/085013. |
[18] |
M. Ikehata, Extracting the geometry of an obstacle and a zeroth-order coefficient of a boundary condition via the enclosure method using a single reflected wave over a finite time interval, Inverse Problems, 30 (2014), 045011, 24pp.
doi: 10.1088/0266-5611/30/4/045011. |
[19] |
M. Ikehata and H. Itou, On reconstruction of a cavity in a linearized viscoelastic body from infinitely many transient boundary data, Inverse Problems, 28 (2012), 125003, 19pp.
doi: 10.1088/0266-5611/28/12/125003. |
[20] |
M. Ikehata and M. Kawashita, On the reconstruction of inclusions in a heat conductive body from dynamical boundary data over a finite time interval, Inverse Problems, 26 (2010), 095004, 15pp.
doi: 10.1088/0266-5611/26/9/095004. |
[21] |
V. Isakov, Inverse obstacle problems, Topical review, Inverse Problems, 25 (2009), 123002, 18pp.
doi: 10.1088/0266-5611/25/12/123002. |
[22] |
P. D. Lax and R. S. Phillips, The scattering of sound waves by an obstacle, Comm. Pure and Appl. Math., 30 (1977), 195-233.
doi: 10.1002/cpa.3160300204. |
[23] |
H. Liu, M. Yamamoto and J. Zou, Reflection principle for the Maxwell equations and its application to inverse electromagnetic scattering, Inverse Problems, 23 (2007), 2357-2366.
doi: 10.1088/0266-5611/23/6/005. |
[24] |
A. Majda and M. Taylor, Inverse scattering problems for transparent obstacles, electromagnetic waves, and hyperbolic systems, Comm. in Partial Differential Equations, 2 (1977), 395-438.
doi: 10.1080/03605307708820035. |
[25] |
J.-C. Nédélec, Acoustic and Electromagnetic Equations, Integral Representations for Harmonic Problems, Springer, New York, 2001.
doi: 10.1007/978-1-4757-4393-7. |
[26] |
B. O'Neill, Elementary Differential Geometry, Revised, $2^{nd}$ edition, Academic Press, 2006. |
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