Stable determination of sound-hard polyhedral scatterers by a minimal number of scattering measurements

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• 作者：Hongyu Liu^a ; ^{hongyuliu@hkbu.edu.hk} ; Michele Petrini^b ; ^{mpetrini139@yahoo.it} ; Luca Rondi^b ; ^{rondi@units.it} ; Jingni Xiao^a ; ^{xiaojn@live.com}
• 关键词：primary ; 74J20 ; 74J25 ; secondary ; 35R30 ; 35Q74
• 刊名：Journal of Differential Equations
• 出版年：2017
• 出版时间：5 February 2017
• 年：2017
• 卷：262
• 期：3
• 页码：1631-1670
• 全文大小：558 K
• 卷排序：262

文摘

The aim of the paper is to establish optimal stability estimates for the determination of sound-hard polyhedral scatterers in RNRN, N≥2N≥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=2,3N=2,3 and to polyhedral obstacles, that is to polyhedra, then we obtain stability estimates with fewer measurements, namely first with N−1N−1 measurements and then with a single measurement. In this case the dependence on h is not explicit anymore and the modulus of continuity depends on h as well.