非均匀介质中声波的远场分布的性质

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名

邮箱

手机号码

标题

留言内容

验证码

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.

Abstract: In this paper, by using functional analysis and integral equation method, we obtain some results about the properties of far field of acoustic waves in an inhomogeneous medium. And we also discuss some ill-posed inverse scattering problems by Tikhonov regularization method.

[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).