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GLOBAL UNIQUENESS IN THE INVERSE ACOUSTIC SCATTERING PROBLEM WITHIN POLYGONAL OBSTACLES 被引量：2

GLOBAL UNIQUENESS IN THE INVERSE ACOUSTIC SCATTERING PROBLEM WITHIN POLYGONAL OBSTACLES
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摘要 The authors prove the uniqueness in the inverse acoustic scattering problem within convex polygonal domains by a single incident direction in the sound-soft case and the sound-hard case, and by two incident directions in the case of the impedance boundary condition. The proof is based on analytic continuation on a straight line.
作者 CHENGJIN YAMAMOTOMASAHIRO
机构地区 DepartmentofMathematics DepartmentofMathematicalSciences
出处 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2004年第1期1-6,共6页 数学年刊（B辑英文版）
基金 Project supported by the National Natural Science Foundation of China (No.10271032) the Nonlinear Mathematical Models and Methods Laboratory and the Grants 15340027 15654015 from the Japan Society for the Promotion of Science and Sanwa Systems Development Co.Ltd. (Tokyo).
关键词 Inverse scattering UNIQUENESS Convex polygonal domains 全局唯一性 声学 散射 多角形障碍物 边界条件
分类号 O422.5 [理学—声学] O175 [理学—基础数学]
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参考文献18

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同被引文献21

  • 1刘继军,程晋,中村玄.Reconstruction and uniqueness of an inverse scattering problem with impedance boundary[J].Science China Mathematics,2002,45(11):1408-1419. 被引量：7
  • 2WANG HaiBing,LIU JiJun.On the reconstruction of Dirichlet-to-Neumann map in inverse scattering problems with stability estimates[J].Science China Mathematics,2010,53(8):2069-2084. 被引量：2
  • 3Agmon S, Hormander L. Asymptotic properties of solutions of differential equations with simple eharacteristics[J]. Journal D'Analyse Mathematique , 1976,30: 1-37.
  • 4Colton D, Coyle J, Monk P. Recent developments in inverse acoustic scattering theory[J]. SIAM, 2000, 42 : 369-414.
  • 5Colton D, Kress R. Inverse acoustic and electromagnetic scattering theory[M]. 2nd ed. Berlin: Springer- Verlay, 1998.
  • 6Colton D, Kress R. Integral equation methods in scattering theory[M]. N Y: John Wiley and Son, 1983.
  • 7Gintides D. Local uniqueness for the inverse scattering problem in acoustics via the Faber-Krahn inequality [J]. Inverse Problems, 2005,21(4):1195-1205.
  • 8Liu Changmei. An inverse obstacle problem: a uniqueness theorem for balls[J]. Institute for Mathematics and Its Applications, 1997,90: 347.
  • 9Yun K Y. The reflection of solutions of Helmholtz equation and an application[J]. Comm Korean Math Soc, 2000,16(3): 427-436.
  • 10Alessandrini G, Rondi L. Determining a sound-soft polyhedral scatterer by a single farfield measurement [J]. Proceedings of the American Mathrnatical Society, 2005,133(6) : 1685-1691.

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Chinese Annals of Mathematics,Series B
2004年 第1期

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