Publication Cover
Applicable Analysis
An International Journal
Volume 78, 2001 - Issue 3-4
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Original Articles

The unknown object problem in a sea with sloping bottom

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Pages 497-511 | Received 25 Nov 2000, Published online: 23 Jun 2010

References

  • Gilbert , R.P. , Lin , Z. and Buchanan , J.L. 1997 . Direct and inverse problems in ocean acoustics . Nonlinear Analysis , 30 ( 3 ) : 1535 – 1546 .
  • Colton , D. and Kirsch , A. 1996 . A simple method for solving inverse scattering problems in the resonance region . Inverse Problems , 12 : 383 – 393 .
  • Colton , D. and Monk , P. 1998 . A linear sampling method for the detection of leukemi using microwaves . to appear in SIAM J. Applied. Math ,
  • Gilbert , R.P. and Lin , Zhongyan . 1993 . On the conditions for uniqueness and existence of the solution to an acoustic inverse problem: I Theory . J. Computational Acoustics , 1 ( 2 ) : 229 – 247 .
  • Gilbert , R.P. , Mawata , C. and Xu , Y. 2000 . “ Determination of a distributed inhomogeneity in a two-layered waveguide from scattered sound. In: ” . In Direct and Inverse Problems of Mathematical Physics , Edited by: Gilbert et al , R. Kluwer Academic Publishers .
  • Gilbert , R.P. , Scotti , T. , Wirgin , A. and Xu , Y. 1998 . The unidentified object problem in a shallow ocean . J. Acoustic Society of America , 103 ( 3 ) : 1320 – 1327 .
  • Gilbert , R.P. and Xu , Y. 1989 . Starting fields and far fields in ocean acoustics . Wave Motion , 11 : 507 – 524 .
  • Gilbert , R.P. and Xu , Y. 1989 . Dense sets and the projection theorem for acoustic harmonic waves in homogeneous finite depth oceans . Math. Methods Appl. Sci , 12 : 69 – 76 .
  • Gilbert R.P. Xu Y. Generalized Herglotz functions and inverse scattering problems in finite depth oceans 1992 Inverse Problems, SIAM
  • Gilbert , R.P. and Xu , Yongzhi . “ The sea-mount problem. In: ” . In Nonlinear Problem in Applied Mathematics Edited by: Angell et al , T. 140 – 149 . SIAM, Philadelphia
  • Kirsch A. An introduction to the rtlathematical theory of inverse problems Springer 1996
  • Xu Y. Mawata C. Lin W. Generalized Dual Space Indicator Method for Underwater Imaging 2000 Inverse Problems, to appear
  • Xu Y. Uniqueness and computational results for obstacle inverse scattering in a water waveguide 2000 submitted
  • Xu , Y. and Yan , Y. 1993 . An approximate boundary integral equation method for acoustic scattering in shallow oceans . J. Computational Acoustics , 1 ( 1 )

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