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Applicable Analysis
An International Journal
Volume 86, 2007 - Issue 8
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Original Articles

Extracting discontinuity in a heat conductive body. One-space dimensional case

Masaru Ikehata Department of Mathematics, Graduate School of Engineering, Gunma University, Kiryu 376-8515, JapanCorrespondence[email protected]
Pages 963-1005 | Received 01 May 2007, Accepted 19 May 2007, Published online: 24 Sep 2007

Citations (29)

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Read on this site (2)

Aymen Jbalia & Abdessatar Khelifi. (2021) On the identification of the heat conductivity distribution from partial dynamic boundary measurements. Applicable Analysis 100:13, pages 2735-2748.
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P. Gaitan, H. Isozaki, O. Poisson, S. Siltanen & J.P. Tamminen. (2015) Inverse Problems for Time-Dependent Singular Heat Conductivities: Multi-Dimensional Case. Communications in Partial Differential Equations 40:5, pages 837-877.
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Articles from other publishers (27)

Masaru Ikehata. (2023) On finding a penetrable obstacle using a single electromagnetic wave in the time domain. Journal of Inverse and Ill-posed Problems 0:0.
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Masaru Ikehata. (2023) Extracting discontinuity using the probe and enclosure methods. Journal of Inverse and Ill-posed Problems 0:0.
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Masaru Ikehata. (2020) The enclosure method for inverse obstacle scattering over a finite time interval: VI. Using shell-type initial data. Journal of Inverse and Ill-posed Problems 28:3, pages 349-366.
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Masaru Ikehata. (2020) The enclosure method for the heat equation using time-reversal invariance for a wave equation. Journal of Inverse and Ill-posed Problems 28:1, pages 93-104.
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Masaru Ikehata. (2019) Prescribing a heat flux coming from a wave equation. Journal of Inverse and Ill-posed Problems 27:5, pages 731-744.
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Masaru Ikehata. (2018) On finding a cavity in a thermoelastic body using a single displacement measurement over a finite time interval on the surface of the body. Journal of Inverse and Ill-posed Problems 26:3, pages 369-394.
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Masaru Ikehata. (2017) 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. Journal of Inverse and Ill-posed Problems 25:6, pages 747-761.
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Manel Bouraoui, Lassaad El Asmi & Abdessatar Khelifi. (2017) Reconstruction of polygonal inclusions in a heat conductive body from dynamical boundary data. ESAIM: Mathematical Modelling and Numerical Analysis 51:3, pages 949-964.
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Masaru Ikehata & Kiwoon Kwon. (2017) Trusted frequency region of convergence for the enclosure method in thermal imaging. Journal of Inverse and Ill-posed Problems 25:1, pages 81-97.
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M. Bouraoui, L. El Asmi & A. Khelifi. (2016) On an inverse boundary problem for the heat equation when small heat conductivity defects are present in a material. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 96:3, pages 327-343.
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Masaru Ikehata. (2015) On finding an obstacle embedded in the rough background medium via the enclosure method in the time domain. Inverse Problems 31:8, pages 085011.
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Masaru Ikehata. (2014) 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 30:4, pages 045011.
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Masaru Ikehata & Mishio Kawashita. (2014) An inverse problem for a three-dimensional heat equation in thermal imaging and the enclosure method. Inverse Problems & Imaging 8:4, pages 1073-1116.
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Masaru Ikehata. (2013) 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 29:8, pages 085013.
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P. Gaitan, H. Isozaki, O. Poisson, S. Siltanen & J. P. Tamminen. (2013) Inverse Problems for Time-Dependent Singular Heat Conductivities---One-Dimensional Case. SIAM Journal on Mathematical Analysis 45:3, pages 1675-1690.
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Masaru Ikehata & Hiromichi Itou. (2012) On reconstruction of a cavity in a linearized viscoelastic body from infinitely many transient boundary data. Inverse Problems 28:12, pages 125003.
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Masaru Ikehata. (2012) An inverse acoustic scattering problem inside a cavity with dynamical back-scattering data. Inverse Problems 28:9, pages 095016.
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Horst Heck, Gen Nakamura & Haibing Wang. (2012) Linear sampling method for identifying cavities in a heat conductor. Inverse Problems 28:7, pages 075014.
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Masaru Ikehata. (2012) 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 28:4, pages 045010.
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Patricia Gaitan, Hiroshi Isozaki, Olivier Poisson, Samuli Siltanen & Janne Tamminen. (2012) Probing for inclusions in heat conductive bodies. Inverse Problems & Imaging 6:3, pages 423-446.
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Masaru Ikehata. (2011) The framework of the enclosure method with dynamical data and its applications. Inverse Problems 27:6, pages 065005.
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M Ikehata & H Itou. (2011) On reconstruction of an unknown polygonal cavity in a linearized elasticity with one measurement. Journal of Physics: Conference Series 290, pages 012005.
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Masaru Ikehata & Mishio Kawashita. (2010) On the reconstruction of inclusions in a heat conductive body from dynamical boundary data over a finite time interval. Inverse Problems 26:9, pages 095004.
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Masaru Ikehata. (2010) The enclosure method for inverse obstacle scattering problems with dynamical data over a finite time interval. Inverse Problems 26:5, pages 055010.
Crossref
Masaru Ikehata & Mishio Kawashita. (2009) The enclosure method for the heat equation. Inverse Problems 25:7, pages 075005.
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Y. Daido, Y. Lei, J.J. Liu & G. Nakamura. (2009) Numerical implementations of dynamical probe method for non-stationary heat equation. Applied Mathematics and Computation 211:2, pages 510-521.
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M Ikehata & H Itou. (2008) Enclosure method and reconstruction of a linear crack in an elastic body. Journal of Physics: Conference Series 135, pages 012052.
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