On finding a penetrable obstacle using a single electromagnetic wave in the time domain

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), no. 4, 1369–1382. 10.1137/S0036139900373927Search in Google Scholar

[2] N. Bleistein and R. A. Handelsman, Asymptotic Expansions of Integrals, 2nd ed., Dover Publications, New York, 1986. Search in Google Scholar

[3] D. E. Carlson, Linear thermoelasticity, Mechanics of Solids Vol. II, Springer, Berlin (1984), 297–345. 10.1007/978-3-642-69567-4_2Search in Google Scholar

[4] R. Courant and D. Hilbert, Methoden der Mathematischen Physik. Vol. II, Interscience, New York, 1937. 10.1007/978-3-642-47434-7Search in Google Scholar

[5] R. Dautray and J.-L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology. Evolution problems. I, Vol. 5, Springer, Berlin, 1992. Search in Google Scholar

[6] M. Ikehata, Enclosing a polygonal cavity in a two-dimensional bounded domain from Cauchy data, Inverse Problems 15 (1999), no. 5, 1231–1241. 10.1088/0266-5611/15/5/308Search in Google Scholar

[7] M. Ikehata, Reconstruction of the support function for inclusion from boundary measurements, J. Inverse Ill-Posed Probl. 8 (2000), no. 4, 367–378. 10.1515/jiip.2000.8.4.367Search in Google Scholar

[8] M. Ikehata, Extracting discontinuity in a heat conductive body. One-space dimensional case, Appl. Anal. 86 (2007), no. 8, 963–1005. 10.1080/00036810701460834Search in Google Scholar

[9] M. Ikehata, The enclosure method for inverse obstacle scattering problems with dynamical data over a finite time interval, Inverse Problems 26 (2010), no. 5, Article ID 055010. 10.1088/0266-5611/26/5/055010Search in Google Scholar

[10] 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), no. 4, Article ID 045010. 10.1088/0266-5611/28/4/045010Search in Google Scholar

[11] M. Ikehata, On finding an obstacle embedded in the rough background medium via the enclosure method in the time domain, Inverse Problems 31 (2015), no. 8, Article ID 085011. 10.1088/0266-5611/31/8/085011Search in Google Scholar

[12] M. Ikehata, The enclosure method for inverse obstacle scattering using a single electromagnetic wave in time domain, Inverse Probl. Imaging 10 (2016), no. 1, 131–163. 10.3934/ipi.2016.10.131Search in Google Scholar

[13] M. Ikehata, A remark on finding the coefficient of the dissipative boundary condition via the enclosure method in the time domain, Math. Methods Appl. Sci. 40 (2017), no. 4, 915–927. 10.1002/mma.4021Search in Google Scholar

[14] M. Ikehata, On finding an obstacle with the Leontovich boundary condition via the time domain enclosure method, Inverse Probl. Imaging 11 (2017), no. 1, 99–123. 10.3934/ipi.2017006Search in Google Scholar

[15] M. Ikehata, The enclosure method for inverse obstacle scattering over a finite time interval: IV. Extraction from a single point on the graph of the response operator, J. Inverse Ill-Posed Probl. 25 (2017), no. 6, 747–761. 10.1515/jiip-2016-0023Search in Google Scholar

[16] M. Ikehata, On finding a cavity in a thermoelastic body using a single displacement measurement over a finite time interval on the surface of the body, J. Inverse Ill-Posed Probl. 26 (2018), no. 3, 369–394. 10.1515/jiip-2017-0066Search in Google Scholar

[17] M. Ikehata, On finding the surface admittance of an obstacle via the time domain enclosure method, Inverse Probl. Imaging 13 (2019), no. 2, 263–284. 10.3934/ipi.2019014Search in Google Scholar

[18] M. Ikehata, The enclosure method for inverse obstacle scattering over a finite time interval: V. Using time-reversal invariance, J. Inverse Ill-Posed Probl. 27 (2019), no. 1, 133–149. 10.1515/jiip-2018-0046Search in Google Scholar

[19] M. Ikehata, The enclosure method for inverse obstacle scattering over a finite time interval: VI. Using shell-type initial data, J. Inverse Ill-Posed Probl. 28 (2020), no. 3, 349–366. 10.1515/jiip-2019-0039Search in Google Scholar

[20] M. Ikehata and M. Kawashita, On finding a buried obstacle in a layered medium via the time domain enclosure method, Inverse Probl. Imaging 12 (2018), no. 5, 1173–1198. 10.3934/ipi.2018049Search in Google Scholar

[21] M. Ikehata, M. Kawashita and W. Kawashita, On finding a buried obstacle in a layered medium via the time domain enclosure method in the case of possible total reflection phenomena, Inverse Probl. Imaging 13 (2019), no. 5, 959–981. 10.3934/ipi.2019043Search in Google Scholar

[22] A. Kirsch and N. Grinberg, The Factorization Method for Inverse Problems, Oxford Lecture Ser. Math. Appl. 36, Oxford University, Oxford, 2008. 10.1093/acprof:oso/9780199213535.001.0001Search in Google Scholar

[23] H.-M. Nguyen and V. Vinoles, Electromagnetic wave propagation in media consisting of dispersive metamaterials, C. R. Math. Acad. Sci. Paris 356 (2018), no. 7, 757–775. 10.1016/j.crma.2018.05.012Search in Google Scholar

[24] H.-M. Nguyen and M. S. Vogelius, Approximate cloaking using transformation optics for acoustic and electromagnetic waves, Acta Math. Vietnam. 45 (2020), no. 1, 261–280. 10.1007/s40306-019-00334-5Search in Google Scholar

[25] B. O’Neill, Elementary Differential Geometry, 2nd ed., Elsevier/Academic Press, Amsterdam, 2006. Search in Google Scholar