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Coefficient inverse problems for partial differential equations in the viscoelasticity, the material science and population dynamics by Carleman estimates
https://doi.org/10.15083/00004036
https://doi.org/10.15083/0000403698699e8d-5596-476e-9e26-8d9a4c270c85
| 名前 / ファイル | ライセンス | アクション |
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UesakaM_23_3_PhD_a.pdf (1.1 MB)
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UesakaM_23_3_PhD_b.pdf (63.1 kB)
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| Item type | 学位論文 / Thesis or Dissertation(1) | |||||
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| 公開日 | 2012-10-23 | |||||
| タイトル | ||||||
| タイトル | Coefficient inverse problems for partial differential equations in the viscoelasticity, the material science and population dynamics by Carleman estimates | |||||
| 言語 | ||||||
| 言語 | eng | |||||
| 資源タイプ | ||||||
| 資源 | http://purl.org/coar/resource_type/c_46ec | |||||
| タイプ | thesis | |||||
| ID登録 | ||||||
| ID登録 | 10.15083/00004036 | |||||
| ID登録タイプ | JaLC | |||||
| その他のタイトル | ||||||
| その他のタイトル | カーレマン評価を用いた、粘弾性論・材料科学・個体群動態学における偏微分方程式系の係数決定逆問題について | |||||
| 著者 |
Uesaka, Masaaki
× Uesaka, Masaaki |
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| 著者別名 | ||||||
| 識別子Scheme | WEKO | |||||
| 識別子 | 9335 | |||||
| 姓名 | 上坂, 正晃 | |||||
| 著者所属 | ||||||
| 著者所属 | 東京大学大学院数理科学研究科 | |||||
| 著者所属 | ||||||
| 著者所属 | Graduate School of Mathematical Sciences, The University of Tokyo | |||||
| Abstract | ||||||
| 内容記述タイプ | Abstract | |||||
| 内容記述 | In this paper, we consider coefficient inverse problems in the viscoelasticity,the material science and the population studies and prove the stability ofthese problem by an a priori weighted L2-norm estimate which is called aCarleman estimate.In Chapter 1, an inverse problem of determining coefficients in a viscoelasticmodel which is called Kelvin-Voigt model is discussed. The dataavailable to us is a Cauchy data on subboundary. We prove that with twoappropriate measurements, we can obtain a Holder stability estimate of the inverse problem.In Chapter 2, we discuss the determination of a thermal conductivity anda mobility in the linearized phase field model with measurement of only onecomponent in a small domain. Our result is the Lipschitz stability estimate of this problem.In Chapter 3, we consider the coefficient inverse problem of the structuredpopulation model. In the structured population model, an age andan individual size as well as a spatial position and time are considered asindepenent variables and then the equation has a special form. We prove a Carleman estimate for this equation and obtain a stability estimate for theinverse problem. | |||||
| 書誌情報 | 発行日 2011-03-24 | |||||
| 日本十進分類法 | ||||||
| 主題Scheme | NDC | |||||
| 主題 | 410 | |||||
| 学位名 | ||||||
| 学位名 | 博士(数理科学) | |||||
| 学位 | ||||||
| 値 | doctoral | |||||
| 学位分野 | ||||||
| Mathematical Sciences (数理科学) | ||||||
| 学位授与機関 | ||||||
| 学位授与機関名 | University of Tokyo (東京大学) | |||||
| 研究科・専攻 | ||||||
| Graduate School of Mathematical Sciences (数理科学研究科) | ||||||
| 学位授与年月日 | ||||||
| 学位授与年月日 | 2011-03-24 | |||||
| 学位授与番号 | ||||||
| 学位授与番号 | 甲第27184号 | |||||
| 学位記番号 | ||||||
| 博数理第365号 | ||||||
