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

Cheng Jin

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 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.

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.

PDF( 461 KB)

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

Cheng Jin

Mathematics Institute, Fudan University, Shanghai

Received Date: 1989-08-04
Publish Date: 1990-08-15

Abstract

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.

FullText(HTML)

References(12)

References

[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).