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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 王振男(Jenn_Nan Wang) | |
| dc.contributor.author | Chia-Hung Lin | en |
| dc.contributor.author | 林嘉宏 | zh_TW |
| dc.date.accessioned | 2021-05-12T09:35:40Z | - |
| dc.date.available | 2018-11-19 | |
| dc.date.available | 2021-05-12T09:35:40Z | - |
| dc.date.copyright | 2018-11-19 | |
| dc.date.issued | 2018 | |
| dc.date.submitted | 2018-08-20 | |
| dc.identifier.citation | [1] Robert A Adams and John JF Fournier. Sobolev spaces, volume 140 of Pure and Applied Mathematics. Elsevier/Academic Press, 2003.
[2] Shmuel Agmon, Avron Douglis, and Louis Nirenberg. Estimates near the boundary for solutions of elliptic partial di erential equations satisfying general boundary conditions ii. Communications on Pure and Applied Mathematics, 17(1):35{92, 1964. [3] Giovanni Alessandrini, Antonino Morassi, and Edi Rosset. Detecting an inclusion in an elastic body by boundary measurements. SIAM Journal on Mathematical Analysis, 33(6):1247{1268, 2002. [4] Giovanni Alessandrini, Antonino Morassi, and Edi Rosset. Detecting an inclusion in an elastic body by boundary measurements. SIAM review, 46(3):477{498, 2004. [5] M Di Cristo, CL Lin, S Vessella, and JN Wang. Detecting a general inclusion in the shallow shell. SIAM J. Math. Analysis, 45:88{100, 2013. [6] Mariano Giaquinta and Luca Martinazzi. An introduction to the regu-larity theory for elliptic systems, harmonic maps and minimal graphs. Springer Science & Business Media, 2013. [7] David Gilbarg and Neil S Trudinger. Elliptic partial differential equations of second order, volume 224. Springer Verlag, 2001. [8] S onke Hansen and Gunther Uhlmann. Propagation of polarization in elastodynamics with residual stress and travel times. Mathematische Annalen, 326(3):563{587, 2003. [9] Anne Hoger. On the determination of residual stress in an elastic body. Journal of Elasticity, 16(3):303{324, 1986. [10] Ching-Lung Lin and Jenn-Nan Wang. Optimal three-ball inequalities and quantitative uniqueness for the stokes system. arXiv preprint arXiv:0812.3730, 2008. [11] Jacques Louis Lions, Enrico Magenes, and P Kenneth. Non-homogeneous boundary value problems and applications, volume 1. Springer Berlin, 1972. [12] Chi-Sing Man. Hartig's law and linear elasticity with initial stress. Inverse Problems, 14(2):313, 1998. [13] Antonino Morassi, Edi Rosset, and Sergio Vessella. Detecting general inclusions in elastic plates. Inverse Problems, 25(4):045009, 2009. [14] Antonino Morassi, Edi Rosset, and Sergio Vessella. Sharp three sphere inequality for perturbations of a product of two second order elliptic operators and stability for the cauchy problem for the anisotropic plate equation. Journal of Functional Analysis, 261(6):1494{1541, 2011. [15] Lizabeth V Rachele. Uniqueness in inverse problems for elastic media with residual stress. Communications in Partial Di erential Equations, 28(11-12):1787{1806, 2003. [16] RL Robertson. Boundary identi ability of residual stress via the dirichlet to neumann map. Inverse Problems, 13(4):1107, 1997. [17] Edi Rosset and Giovanni Alessandrini. The inverse conductivity problem with one measurement: bounds on the size of the unknown object. SIAM Journal on Applied Mathematics, 58(4):1060{1071, 1998. [18] Gunther Uhlmann and Jenn-Nan Wang. Unique continuation property for the elasticity with general residual stress. Inverse Probl. Imaging, 3(2):309{317, 2009. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/handle/123456789/1292 | - |
| dc.description.abstract | 我們考慮估計內含物大小(D)的反問題，在有殘餘應力的彈性系統中(Ω,D⊂Ω)，由於存在殘餘應力，所以該彈性系統的結構方程式不是各方向同性的，我們證明，透過量測Ω邊界之應力與位移量，可得內含物尺寸上下界的估計。 | zh_TW |
| dc.description.abstract | We only consider the inverse problem for estimating the size of an inclusion D, D⊂Ω, in an elastic body with residual stress. The constitutive equation of this elasticity system is not isotropic, due to the presence of residual stresses. We prove that the size of the inclusion can be estimated both from above and below by using only one pair of traction-displacement measurement on the boundary of Omega. | en |
| dc.description.provenance | Made available in DSpace on 2021-05-12T09:35:40Z (GMT). No. of bitstreams: 1 ntu-107-D98221001-1.pdf: 836198 bytes, checksum: e00e44c7844cd6082d2006f5b0ba6cb4 (MD5) Previous issue date: 2018 | en |
| dc.description.tableofcontents | 1 Introduction 4
1.1 Elasticity system with residual stress . . . . . . . . . . . . . . 4 1.2 Inverse problem . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Estimate size of an inclusion in an elastic body with residual stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2 Elementary concepts and notations 10 2.1 Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2 Sobolev spaces . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3 Assumptions and main result 13 3.1 Aussumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.2 Main result(theorem) . . . . . . . . . . . . . . . . . . . . . . . 15 3.3 Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 4 Standard estimate tools 17 4.1 Interior estimate . . . . . . . . . . . . . . . . . . . . . . . . . 17 4.2 Caccioppoli-type inequality . . . . . . . . . . . . . . . . . . . 20 4.3 Poincare inequality . . . . . . . . . . . . . . . . . . . . . . . . 22 4.4 Sobolev inequality . . . . . . . . . . . . . . . . . . . . . . . . 25 5 Transformation of the original system into two new systems 27 5.1 Auxiliary new system . . . . . . . . . . . . . . . . . . . . . . . 27 5.2 New system for the product of two elliptic operators . . . . . . 28 6 Carleman estimates 29 6.1 Second order type Carleman estimate . . . . . . . . . . . . . . 30 6.2 Auxiliary Carleman estimate form . . . . . . . . . . . . . . . . 31 6.3 Production of two second order type Carleman estimate . . . . 32 7 Three spheres inequalities 35 7.1 Three spheres inequality - normal type . . . . . . . . . . . . . 35 7.2 Three spheres inequality - differential type . . . . . . . . . . . 39 8 Lipschitz propagation of smallness 40 8.1 Boundary estimate . . . . . . . . . . . . . . . . . . . . . . . . 40 8.2 Theorem of Lipschitz propagation of smallness . . . . . . . . . 41 9 Auxiliary lemmas 43 9.1 Three auxiliary equations . . . . . . . . . . . . . . . . . . . . 43 9.2 Estimate boundary energy of strongly elliptic system . . . . . 45 10 Proof of main result 49 11 Further work 51 12 References 53 | |
| dc.language.iso | en | |
| dc.subject | 彈性系統 | zh_TW |
| dc.subject | 利普希茨之小的傳播 | zh_TW |
| dc.subject | 三球不等式 | zh_TW |
| dc.subject | 卡爾曼估計 | zh_TW |
| dc.subject | 殘餘應力 | zh_TW |
| dc.subject | 反問題 | zh_TW |
| dc.subject | 檢測內在異質物體 | zh_TW |
| dc.subject | Three-Sphere inequality | en |
| dc.subject | Lipschitz propagation of smallness | en |
| dc.subject | Inverse Problem | en |
| dc.subject | Detecting inclusions | en |
| dc.subject | Elasticity system | en |
| dc.subject | Residual stress | en |
| dc.subject | Carleman estimate | en |
| dc.title | 檢測有殘餘應力的彈性物體中內含物大小 | zh_TW |
| dc.title | Detecting an Inclusion in an Elastic Body with Residual Stress | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 107-1 | |
| dc.description.degree | 博士 | |
| dc.contributor.oralexamcommittee | 林景隆(Ching-Lung Lin),李國明(Kuo-Ming Lee),林太家(Tai-Chia Lin),陳俊全(Chiun-Chuan Chen) | |
| dc.subject.keyword | 反問題,檢測內在異質物體,彈性系統,殘餘應力,卡爾曼估計,三球不等式,利普希茨之小的傳播, | zh_TW |
| dc.subject.keyword | Inverse Problem,Detecting inclusions,Elasticity system,Residual stress,Carleman estimate,Three-Sphere inequality,Lipschitz propagation of smallness, | en |
| dc.relation.page | 54 | |
| dc.identifier.doi | 10.6342/NTU201804025 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2018-08-20 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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