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非均匀介质中声波的远场分布的性质

程晋

程晋. 非均匀介质中声波的远场分布的性质[J]. 应用数学和力学, 1990, 11(8): 739-746.
引用本文: 程晋. 非均匀介质中声波的远场分布的性质[J]. 应用数学和力学, 1990, 11(8): 739-746.
Cheng Jin. Some Properties of Far Field Patterns of Acoustic Waves in an lnhomogeneous Medium[J]. Applied Mathematics and Mechanics, 1990, 11(8): 739-746.
Citation: Cheng Jin. Some Properties of Far Field Patterns of Acoustic Waves in an lnhomogeneous Medium[J]. Applied Mathematics and Mechanics, 1990, 11(8): 739-746.

非均匀介质中声波的远场分布的性质

基金项目: 上海市青年科学基金资助项目;上海市科技发展基金部分资助

Some Properties of Far Field Patterns of Acoustic Waves in an lnhomogeneous Medium

  • 摘要: 本文运用泛函分析和积分方程的方法,讨论了非均匀介质中声波的远场分布的性质,并应用Тихонов正则化方法讨论了不适定的逆散射问题.
  • [1] Colton,D.,Far field patterns for the impendence boundary value problem in acoustic scattering,Applicable Analysis,16(1983),131-139.
    [2] Colton,D.and A.Kirch,Dense sets and far field patterns in acoustic wave propagation,SIAM J.Math.Anal.,15(1984),996-1006.
    [3] Colton,D.and P.Monk,The inverse scattering problem for time harmonic acoustic waves in a penetrable medium,Quart.J.Mech.Appl.Math.,40(1987),189-212.
    [4] Colton,D.,Dense sets and far field patterns for acoustic waves in an inhomogeneous medium,Proc.Edinourgh Math.Soc.,31(1988),401-407.
    [5] Yagle,Andrew E.,Differential and integral methods for multidimensional inverse scattering problems,J.Math.Phys.,27(1986),2584-2591.
    [6] Reed,M.and B.Simon,Methods of Modern Mathematical Physics,I.Functional Analysis,Academic Press,New York(1972).
    [7] Gilbert,R.P.,Function Theoretic Methods in Partial Differential Equations,Academic Press,New York,London(1969).
    [8] Ramm,A.g.,Multidimensional inverse problems and completeness of the products of solutions to PDE,J.Math.Anal.Appl.,134(1988),211-253.
    [9] Tikhonov,A.and V.Arsenin,Solution of Ill-posed Problems,Winston,Washington(1977).
    [10] Cheng Jin,Modification of Tikhonov regularization method for ill-posed problems,J.Math.,9,1(1989),13-22.
    [11] Cheng Jin,Convergence rate of Arcangeli's method for Tikhonov regularization in Hilbert scales,Applied Math.,A Journal of Chinese Universities,2(1987),400-409.
    [12] Ramm,A.G.,Scattering by Obstacles,Reidel,Dordrecht(1986).
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出版历程
  • 收稿日期:  1989-08-04
  • 刊出日期:  1990-08-15

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