Name
Abstract | ||
|---|---|---|
The authors recently introduced a constructive method for solving the inverse obstacle problem and the inverse inhomogeneous medium problem for acoustic waves [D. Colton and P. Monk, SIAM J. Sci. Statist. Comput., 8 (1987), pp. 278-291], [D. Colton and P. Monk, Quart. J. Mech. Appl. Math., 41 (1988), pp. 97-125]. If F(theta; alpha) is the far field pattern corresponding to the incident field exp [ikr cos (theta - alpha)] with wave number k > 0, their method is based on the fact that the integral operator K:L2[-pi, pi] --> L2[-pi, pi] defined by Kg = integral-pi/-pi F(theta; alpha)g(theta) dtheta is injective and has dense range. Unfortunately, there can exist values of k such that this is not the case for either of the inverse problems considered in the above-mentioned references. Motivated by an idea of Douglas Jones for the direct obstacle problem for acoustic waves [D. Jones, Quart. J. Mech. Appl. Math., 27 (1974), pp. 129-142], it is shown how to modify the operator K such that the modified operator is injective with dense range for all values of k > 0. The proof of this shows how the method of Colton and Monk can be modified to be applicable for all positive values of the wave number k. |
Year | DOI | Venue |
|---|---|---|
1993 | 10.1137/0153041 | SIAM Journal of Applied Mathematics |
Keywords | Field | DocType |
inverse scattering theory,integral equation,acoustic waves,inverse scattering | Pi,Inverse,Scattering theory,Injective function,Mathematical physics,Quantum mechanics,Mathematical analysis,Integral equation,Inverse problem,Obstacle problem,Inverse scattering problem,Physics | Journal |
Volume | Issue | ISSN |
53 | 3 | 0036-1399 |
Citations | PageRank | References |
1 | 1.30 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| David Colton | 1 | 33 | 15.98 |
| Peter Monk | 2 | 230 | 72.81 |