Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
T. S. Angell, D. Colton, and A. Kirsch, The three dimensional inverse scattering problem for acoustic waves, J. Diff. Eqns., to appear.
M. Bertero, C. de Mol, and G. A. Viano, The stability of inverse problems, in Inverse Scattering Problems in Optics, H. P. Baltes, editor, Springer-Verlag, Berlin, 1980, 161–214.
D. Colton, Analytic Theory of Partial Differential Equations, Pitman Publishing, London, 1980.
D. Colton, The inverse scattering problem for a cylinder, Proc. Royal Soc. Edinburgh 84A (1979), 135–143
D. Colton, Runge's theorem and far field patterns for the impedance boundary value problem in acoustic wave propagation, SIAM J. Math. Anal., to appear.
D. Colton, Stable methods for determining the surface impedance of an obstacle from low frequency far field data, submitted for publication.
D. Colton and A. Kirsch, Stable methods for solving the inverse scattering problem for a cylinder, Proc. Royal Soc. Edinburgh 89A (1981), 181–188
D. Colton and A. Kirsch, The determination of the surface impedance of an obstacle from measurements of the far field pattern, SIAM J. Applied Math. 41 (1981), 8–15.
D. Colton and R. Kleinman, The direct and inverse scattering problems for an arbitrary cylinder: Dirichlet boundary conditions, Proc. Royal Soc. Edinburgh 86A (1980), 29–42
D. Colton and R. Kress, Integral Equation Methods in Scattering Theory, John Wiley, New York, to appear.
D. Colton and R. Kress, Iterative methods for solving the exterior Dirichlet problem for the Helmholtz equation with applications to the inverse scattering problem for low frequency acoustic waves, J. Math. Anal. Appl. 77 (1980), 60–72.
D. Colton and R. Kress, The impedance boundary value problem for the time harmonic Maxwell equations, Math. Methods in Applied Sciences 3 (1981), 475–487.
D. Colton and R. Kress, The unique solvability of the null field equations of acoustics, Quart. J. Mech. Applied Math., to appear.
S. I. Hariharan, Inverse scattering for an exterior Dirichlet problem, Quart. Applied Math., to appear.
G. Hellwig, Partial Differential Equations, Blaisdell, New York, 1964.
A. Kirsch, Habilitation Dissertation, University of Göttingen, in preparation.
P. D. Lax and R. S. Phillips, Scattering Theory, Academic Press, New York, 1967.
A. Roger, Newton-Kantorovitch algorithm applied to an electromagnetic inverse problem, IEEE Trans. Antennas and Prop. AP-29 (1981), 232–238.
B. D. Sleeman, The inverse problem of acoustic scattering, IMA J. Applied Math., to appear.
B. D. Sleeman, Two-dimensional inverse scattering and conformal mappings, IMA J. Applied Math. 27 (1981), 19–31.
R. Smith, Ph.D. Thesis, University of Delaware, in preparation.
F. Ursell, On the exterior problems of acoustics, Proc. Camb. Phil. Soc. 74 (1973), 117–125.
Editor information
Rights and permissions
Copyright information
© 1982 Springer-Verlag
About this paper
Cite this paper
Colton, D. (1982). The inverse scattering problem for acoustic waves. In: Everitt, W., Sleeman, B. (eds) Ordinary and Partial Differential Equations. Lecture Notes in Mathematics, vol 964. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0064995
Download citation
DOI: https://doi.org/10.1007/BFb0064995
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-11968-5
Online ISBN: 978-3-540-39561-4
eBook Packages: Springer Book Archive