A novel method in determining a layered periodic structure. (English) Zbl 1487.35442
Summary: This paper is concerned with the inverse scattering of time-harmonic waves by a penetrable structure. By applying the integral equation method, we establish the uniform \(L^p_{\alpha}\) (\(1< p\leq 2\)) estimates for the scattered and transmitted wave fields corresponding to a series of incident point sources. Based on these a priori estimates and a mixed reciprocity relation, we prove that the penetrable structure can be uniquely identified by means of the scattered field measured only above the structure induced by a countably infinite number of quasi-periodic incident plane waves.
MSC:
| 35R30 | Inverse problems for PDEs |
| 35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
| 35J25 | Boundary value problems for second-order elliptic equations |
| 35P25 | Scattering theory for PDEs |
| 78A46 | Inverse problems (including inverse scattering) in optics and electromagnetic theory |
| 78A45 | Diffraction, scattering |
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