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

References

• Avdonin , S , Belishev , M and Rozhkov , Y . 1997 . The BC-method in the inverse problem for the heat equation . Journal of Inverse and Ill-Posed Problems , 5 : 309 – 322 .
   Google Scholar
• Bryan , K and Caudill , LF Jr . 1997 . “ Uniqueness for a boundary identification problem in thermal imaging, Differential Equations and Computational Simulations III ” . In Electronic Journal of Differential Equations, Conference 01 Edited by: Graef , J , Shivaji , R , Soni , B and Zhu , J . 23 – 39 . URL: http://www.ma.hw.ac.uk/EJDE/index.html
   Google Scholar
• Canuto , B , Rosset , E and Vessella , S . 2002 . Quantitative estimate of unique continuation for parabolic equations and inverse initial-boundary value problems with unknown boundaries . Transactions of American Mathematical Society , 354 : 491 – 535 .
   Web of Science ®Google Scholar
• Dautray , R and Lions , J-L . 1992 . Mathematical Analysis and Numerical Methods for Science and Technology, 5, Evolution Problems I , Berlin : Springer .
   Google Scholar
• Friedman , A and Isakov , V . 1989 . On the uniqueness in the inverse conductivity problem with one measurement . Indiana University Mathematics Journal , 38 : 563 – 579 .
   Web of Science ®Google Scholar
• Ikehata , M . 1998 . Reconstruction of the shape of the inclusion by boundary measurements . Communications in Partial Differential Equations , 23 : 1459 – 1474 .
   Web of Science ®Google Scholar
• Ikehata , M . 1999 . Enclosing a polygonal cavity in a two-dimensional bounded domain from Cauchy data . Inverse Problems , 15 : 1231 – 1241 .
   Google Scholar
• Ikehata , M . 2000 . Reconstruction of the support function for inclusion from boundary measurements . Journal of Inverse Ill-Posed Problems , 8 : 367 – 378 .
   Google Scholar
• Ikehata , M . 2000 . On reconstruction in the inverse conductivity problem with one measurement . Inverse Problems , 16 : 785 – 793 .
   Web of Science ®Google Scholar
• Ikehata , M . 2002 . A regularized extraction formula in the enclosure method . Inverse Problems , 18 : 435 – 440 .
   Google Scholar
• Ikehata , M . 2003 . Extracting the convex hull of an unknown inclusion in the multilayered material . Applicable Analysis , 82 ( 9 ) : 857 – 873 .
   Google Scholar
• Ikehata , M . 2003 . Exponentially growing solutions, multilayered anisotropic material and the enclosure method . Inverse Problems , 19 : 1065 – 1079 .
   Google Scholar
• Ikehata , M . 2005 . A new formulation of the probe method and related problems . Inverse Problems , 21 : 413 – 426 .
   Google Scholar
• Ikehata , M . 2007 . An inverse source problem for the heat equation and the enclosure method . Inverse Problems , 23 : 183 – 202 .
   Web of Science ®Google Scholar
• Ikehata , M . “ Virtual signal in the heat equation and the enclosure method. ” . In Proceedings of Inverse Problems in Applied Sciences-towards breakthrough-, Journal of Physics: Conference Series (to appear)
   Google Scholar
• Ikehata , M and Ohe , T . 2002 . Numerical method for finding the convex hull of polygonal cavities using enclosure method . Inverse Problems , 18 : 111 – 124 .
   Google Scholar
• Ikehata , M and Ohe , T . 2002 . “ A numerical method for finding the convex hull of inclusions using the enclosure method ” . In Electromagnetic Nondestructive Evaluation (VI) (Studies in Applied Electromagnetics and Mechanics, Vol. 23) , Edited by: Kojima , F , Takagi , T , Udpa , SS and Pavo , J . 21 – 28 . Amsterdam : IOS Press .
   Google Scholar
• Jost , J . 2002 . “ Partial Differential Equations ” . In Graduate Texts in Mathematics , New York : Springer . 214 in series
   Google Scholar
• 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 .
   Web of Science ®Google Scholar
• Kirsch , A . 2000 . New characterizations of solutions in inverse scattering theory . Applicable Analysis , 76 : 319 – 350 .
   Google Scholar
• Naimark , MA . 1967 . Linear Differential Operators parts I , Engl. Transl.) (New York : Ungar .
   Google Scholar
• Olver , FW . 1974 . Asymptotics and Special Functions , New York : Academic Press .
   Google Scholar
• Vessella , S . 1995 . A domain identification problem for the heat equation-Hölder stability estimate . Journal of Inverse Ill-posed Problems , 3 : 495 – 503 .
   Google Scholar
• Vessella , S . 1997 . Stability estimates in an inverse problem for a three-dimensional heat equation . SIAM Journal on Mathematical Analysis , 28 : 1354 – 1370 .
   Web of Science ®Google Scholar