• Previous Article
    Increasing stability for determining the potential in the Schrödinger equation with attenuation from the Dirichlet-to-Neumann map
  • IPI Home
  • This Issue
  • Next Article
    An inverse problem for a three-dimensional heat equation in thermal imaging and the enclosure method
November  2014, 8(4): 1117-1137. doi: 10.3934/ipi.2014.8.1117

Calderón problem for Maxwell's equations in cylindrical domain

1. 

Department of Mathematics, Colorado State University,101 Weber Building, Fort Colins, CO 80523-1784, United States

2. 

Department of Mathematical Sciences, The University of Tokyo, Komaba Meguro Tokyo 153-8914

Received  December 2013 Revised  September 2014 Published  November 2014

We prove some uniqueness results in determination of the conductivity, the permeability and the permittivity of Maxwell's equations in a cylindrical domain $\Omega \times (0,L)$ from partial boundary map. More specifically, for an arbitrarily given subboundary $\Gamma_0 \subset \partial\Omega$, we prove that the coefficients of Maxwell's equations can be uniquely determined in the subdomain $(\Omega \setminus$ [the convex hull of $\Gamma_0])$ $ \times (0,L)$ by the boundary map only for inputs vanishing on $\Gamma_0 \times (0,L)$.
Citation: Oleg Yu. Imanuvilov, Masahiro Yamamoto. Calderón problem for Maxwell's equations in cylindrical domain. Inverse Problems & Imaging, 2014, 8 (4) : 1117-1137. doi: 10.3934/ipi.2014.8.1117
References:
[1]

Duke Math. J., 55 (1987), 943-948. doi: 10.1215/S0012-7094-87-05547-5.  Google Scholar

[2]

in Seminar on Numerical Analysis and its Applications to Continuum Physics, 65-73, Soc. Brasil. Mat., Río de Janeiro, 1980.  Google Scholar

[3]

Comm. P.D.E., 34 (2009), 1425-1464. doi: 10.1080/03605300903296272.  Google Scholar

[4]

Springer-Verlag, Berlin, 1990.  Google Scholar

[5]

Springer-Verlag, Berlin, 2011. doi: 10.1007/978-1-4419-6055-9.  Google Scholar

[6]

J. Amer. Math. Soc., 23 (2010), 655-691. doi: 10.1090/S0894-0347-10-00656-9.  Google Scholar

[7]

Inverse Problems , 29 (2013), 045002, 8pp. doi: 10.1088/0266-5611/29/4/045002.  Google Scholar

[8]

Milan J. Math., 81 (2013), 187-258. doi: 10.1007/s00032-013-0205-3.  Google Scholar

[9]

Inverse Problems and Imaging, 1 (2007), 95-105. doi: 10.3934/ipi.2007.1.95.  Google Scholar

[10]

Mathematical Subject Classification, 6 (2013), 2003-2048. arXiv:1211.1054. doi: 10.2140/apde.2013.6.2003.  Google Scholar

[11]

Ann. of Math., 143 (1996), 71-96. doi: 10.2307/2118653.  Google Scholar

[12]

Duke . Math. J., 70 (1993), 617-653. doi: 10.1215/S0012-7094-93-07014-7.  Google Scholar

[13]

Ann. of Math., 125 (1987), 153-169. doi: 10.2307/1971291.  Google Scholar

show all references

References:
[1]

Duke Math. J., 55 (1987), 943-948. doi: 10.1215/S0012-7094-87-05547-5.  Google Scholar

[2]

in Seminar on Numerical Analysis and its Applications to Continuum Physics, 65-73, Soc. Brasil. Mat., Río de Janeiro, 1980.  Google Scholar

[3]

Comm. P.D.E., 34 (2009), 1425-1464. doi: 10.1080/03605300903296272.  Google Scholar

[4]

Springer-Verlag, Berlin, 1990.  Google Scholar

[5]

Springer-Verlag, Berlin, 2011. doi: 10.1007/978-1-4419-6055-9.  Google Scholar

[6]

J. Amer. Math. Soc., 23 (2010), 655-691. doi: 10.1090/S0894-0347-10-00656-9.  Google Scholar

[7]

Inverse Problems , 29 (2013), 045002, 8pp. doi: 10.1088/0266-5611/29/4/045002.  Google Scholar

[8]

Milan J. Math., 81 (2013), 187-258. doi: 10.1007/s00032-013-0205-3.  Google Scholar

[9]

Inverse Problems and Imaging, 1 (2007), 95-105. doi: 10.3934/ipi.2007.1.95.  Google Scholar

[10]

Mathematical Subject Classification, 6 (2013), 2003-2048. arXiv:1211.1054. doi: 10.2140/apde.2013.6.2003.  Google Scholar

[11]

Ann. of Math., 143 (1996), 71-96. doi: 10.2307/2118653.  Google Scholar

[12]

Duke . Math. J., 70 (1993), 617-653. doi: 10.1215/S0012-7094-93-07014-7.  Google Scholar

[13]

Ann. of Math., 125 (1987), 153-169. doi: 10.2307/1971291.  Google Scholar

[1]

Marion Darbas, Jérémy Heleine, Stephanie Lohrengel. Numerical resolution by the quasi-reversibility method of a data completion problem for Maxwell's equations. Inverse Problems & Imaging, 2020, 14 (6) : 1107-1133. doi: 10.3934/ipi.2020056

[2]

Alexandr Mikhaylov, Victor Mikhaylov. Dynamic inverse problem for Jacobi matrices. Inverse Problems & Imaging, 2019, 13 (3) : 431-447. doi: 10.3934/ipi.2019021

[3]

Armin Lechleiter, Tobias Rienmüller. Factorization method for the inverse Stokes problem. Inverse Problems & Imaging, 2013, 7 (4) : 1271-1293. doi: 10.3934/ipi.2013.7.1271

[4]

Sergei Avdonin, Julian Edward. An inverse problem for quantum trees with observations at interior vertices. Networks & Heterogeneous Media, 2021, 16 (2) : 317-339. doi: 10.3934/nhm.2021008

[5]

Jiangxing Wang. Convergence analysis of an accurate and efficient method for nonlinear Maxwell's equations. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2429-2440. doi: 10.3934/dcdsb.2020185

[6]

Fritz Gesztesy, Helge Holden, Johanna Michor, Gerald Teschl. The algebro-geometric initial value problem for the Ablowitz-Ladik hierarchy. Discrete & Continuous Dynamical Systems, 2010, 26 (1) : 151-196. doi: 10.3934/dcds.2010.26.151

[7]

Enkhbat Rentsen, Battur Gompil. Generalized Nash equilibrium problem based on malfatti's problem. Numerical Algebra, Control & Optimization, 2021, 11 (2) : 209-220. doi: 10.3934/naco.2020022

[8]

Jianli Xiang, Guozheng Yan. The uniqueness of the inverse elastic wave scattering problem based on the mixed reciprocity relation. Inverse Problems & Imaging, 2021, 15 (3) : 539-554. doi: 10.3934/ipi.2021004

[9]

Hildeberto E. Cabral, Zhihong Xia. Subharmonic solutions in the restricted three-body problem. Discrete & Continuous Dynamical Systems, 1995, 1 (4) : 463-474. doi: 10.3934/dcds.1995.1.463

[10]

Hongjie Dong, Xinghong Pan. On conormal derivative problem for parabolic equations with Dini mean oscillation coefficients. Discrete & Continuous Dynamical Systems, 2021  doi: 10.3934/dcds.2021049

[11]

Benjamin Boutin, Frédéric Coquel, Philippe G. LeFloch. Coupling techniques for nonlinear hyperbolic equations. Ⅱ. resonant interfaces with internal structure. Networks & Heterogeneous Media, 2021, 16 (2) : 283-315. doi: 10.3934/nhm.2021007

[12]

Xiaoni Chi, Zhongping Wan, Zijun Hao. A full-modified-Newton step $ O(n) $ infeasible interior-point method for the special weighted linear complementarity problem. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021082

[13]

Alfonso Castro, Jorge Cossio, Sigifredo Herrón, Carlos Vélez. Infinitely many radial solutions for a $ p $-Laplacian problem with indefinite weight. Discrete & Continuous Dynamical Systems, 2021  doi: 10.3934/dcds.2021058

[14]

Yanqin Fang, Jihui Zhang. Multiplicity of solutions for the nonlinear Schrödinger-Maxwell system. Communications on Pure & Applied Analysis, 2011, 10 (4) : 1267-1279. doi: 10.3934/cpaa.2011.10.1267

[15]

Amru Hussein, Martin Saal, Marc Wrona. Primitive equations with horizontal viscosity: The initial value and The time-periodic problem for physical boundary conditions. Discrete & Continuous Dynamical Systems, 2021, 41 (7) : 3063-3092. doi: 10.3934/dcds.2020398

[16]

Michiyuki Watanabe. Inverse $N$-body scattering with the time-dependent hartree-fock approximation. Inverse Problems & Imaging, 2021, 15 (3) : 499-517. doi: 10.3934/ipi.2021002

[17]

Weisong Dong, Chang Li. Second order estimates for complex Hessian equations on Hermitian manifolds. Discrete & Continuous Dynamical Systems, 2021, 41 (6) : 2619-2633. doi: 10.3934/dcds.2020377

[18]

Chonghu Guan, Xun Li, Rui Zhou, Wenxin Zhou. Free boundary problem for an optimal investment problem with a borrowing constraint. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021049

[19]

Giulio Ciraolo, Antonio Greco. An overdetermined problem associated to the Finsler Laplacian. Communications on Pure & Applied Analysis, 2021, 20 (3) : 1025-1038. doi: 10.3934/cpaa.2021004

[20]

Yang Zhang. A free boundary problem of the cancer invasion. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021092

2019 Impact Factor: 1.373

Metrics

  • PDF downloads (36)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]