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Journal article
Stable determination of sound-hard polyhedral scatterers by a minimal number of scattering measurements
Journal of Differential Equations, v 262(3), pp 1631-1670
05 Feb 2017
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Abstract
The aim of the paper is to establish optimal stability estimates for the determination of sound-hard polyhedral scatterers in R-N, N >= 2, by a minimal number of far-field measurements. This work is a significant and highly nontrivial extension of the stability estimates for the determination of sound-soft polyhedral scatterers by far-field measurements, proved by one of the authors, to the much more challenging sound-hard case.
The admissible polyhedral scatterers satisfy minimal a priori assumptions of Lipschitz type and may include at the same time solid obstacles and screen-type components. In this case we obtain a stability estimate with N far-field measurements. Important features of such an estimate are that we have an explicit dependence on the parameter h representing the minimal size of the cells forming the boundaries of the admissible polyhedral scatterers, and that the modulus of continuity, provided the error is small enough with respect to h, does not depend on h. If we restrict to N = 2, 3 and to polyhedral obstacles, that is to polyhedra, then we obtain stability estimates with fewer measurements, namely first with N - 1 measurements and then with a single measurement. In this case the dependence on It is not explicit anymore and the modulus of continuity depends on h as well. (C) 2016 Elsevier Inc. All rights reserved.
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Details
- Title
- Stable determination of sound-hard polyhedral scatterers by a minimal number of scattering measurements
- Creators
- Hongyu Liu - Hong Kong Baptist UniversityMichele Petrini - University of TriesteLuca Rondi - University of TriesteJingni Xiao - Hong Kong Baptist University
- Publication Details
- Journal of Differential Equations, v 262(3), pp 1631-1670
- Publisher
- Elsevier
- Number of pages
- 40
- Grant note
- 11371115 / NSFC; National Natural Science Foundation of China (NSFC) Hong Kong Baptist University (FRG grants) Universita degli Studi di Trieste (FRA) GNAMPA, INdAM; Istituto Nazionale di Alta Matematica (INDAM) 12302415; 405513 / Hong Kong RGC General Research Funds
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000392463100018
- Scopus ID
- 2-s2.0-84994009778
- Other Identifier
- 991021878114404721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Mathematics