請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/58295完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳逸昆(I-Kun Chen) | |
| dc.contributor.author | Yuan-Chieh Chen | en |
| dc.contributor.author | 陳遠介 | zh_TW |
| dc.date.accessioned | 2021-06-16T08:10:34Z | - |
| dc.date.available | 2020-08-24 | |
| dc.date.copyright | 2020-08-24 | |
| dc.date.issued | 2020 | |
| dc.date.submitted | 2020-08-18 | |
| dc.identifier.citation | [1] L. Arkeryd and A. Nouri. l 1 solutions to the stationary boltzmann equation in a slab. Annales de la Facult´ e des sciences de Toulouse : Math´ ematiques, Ser. 6, 9(3):375–413, 2000. [2] C. Cercignani. The Boltzmann Equation and Its Applications. Applied Mathe- matical Sciences. Springer New York, 2012. [3] C. Cercignani, R. Illner, and M. Pulvirenti. The Mathematical Theory of Dilute Gases. Springer, 2014. [4] R. Duan, F. Huang, Y. Wang, and Z. Zhang. Effects of soft interaction and non-isothermal boundary upon long-time dynamics of rarefied gas. Archive for Rational Mechanics and Analysis, 234(2):925–1006, Nov 2019. [5] R. Esposito, Y. Guo, C.-G. Kim, and R. Marra. Non-isothermal boundary in the boltzmann theory and fourier law. Communications in Mathematical Physics, 323:177–239, 2013. [6] R. Esposito, J. L. Lebowitz, and R. Marra. Hydrodynamic limit of the station- ary boltzmann equation in a slab. Commun. Math. Phys., 160, 1994. [7] R. Esposito, J. L. Lebowitz, and R. Marra. The navier-stokes limit of stationary solutions of the nonlinear boltzmann equation. J. Stat. Phys., 78, 1995. [8] L. Evans. Partial Differential Equations. Graduate studies in mathematics. American Mathematical Society, 2010. [9] J. P. Guiraud. Probleme aux limites int´ erieur pour l’´ equation de boltzmann lin´ eaire. J. de M´ ec., 9, 1970. [10] J. P. Guiraud. Probleme aux limites int´ erieur pour l’´ equation de boltzmann en r´ egime stationnaire, faiblement non lin´ eaire. J. de M´ ec., 11, 1972. [11] Y. Guo. Decay and continuity of the boltzmann equation in bounded domains. Archive for Rational Mechanics and Analysis, 197:713–809, 2010. [12] I. Vidav. Spectra of perturbed semigroups with applications to transport theory. J. Math. Anal. Appl., 30, 1970. [13] S.-H. Yu. Stochastic formulation for the initial-boundary value problems of the boltzmann equation. Archive for Rational Mechanics and Analysis, 192:217– 274, 2009. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/58295 | - |
| dc.description.abstract | 波茲曼方程式在研究熱傳導與稀薄氣體的領域中有著重要的地位。本文探討 穩態波茲曼方程式在擴散反射邊界條件下解的存在性，並討論當邊界溫度不為定 值的情形。我們給出一個直接的方法去估計線性化波茲曼算子的核空間，並藉由 此證明了L 2 空間的解存在性與估計。我們也推廣了傳統的特徵線方法，討論了與 邊界多次碰撞的情形，並證明了L ∞ 空間的解存在性與估計。最後，我們證明了 當邊界的溫度與均衡溫度差距小的情形下，穩態波茲曼方程式在邊界非常溫的擴 散反射邊界條件下解的存在性。 | zh_TW |
| dc.description.abstract | In this thesis, we consider the steady Boltzmann equation with diffuse reflection boundary condition. We study the case of hard potential and the non-isothermal boundary. We prove the existence and the uniqueness of solution and their estimate in both L 2 and L ∞ space. In L 2 the Theorem, we provide a direct way to estimate the kernel of the linearized Boltzmann operator. In the L ∞ Theorem, we introduce the stochastic cycles and prove the estimate that is valid for both steady and dynamic cases. And we provide a iteration scheme for the non-isothermal boundary temperature to prove the existence result and the L ∞ estimate when the wall temperature do not oscillate too much. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-16T08:10:34Z (GMT). No. of bitstreams: 1 U0001-1407202002121500.pdf: 1788495 bytes, checksum: f663cfea7f2d8febd5068f8e59147cb4 (MD5) Previous issue date: 2020 | en |
| dc.description.tableofcontents | 口 試 委 員 會 審 定 書 i 誌 謝 ii 中 文 摘 要 iii Abstract 英 文 摘 要 iv 1 Introduction 1 2 Preliminaries 7 2.1 Notations and Background . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Some Basic Properties and Lemmas . . . . . . . . . . . . . . . . . . . 8 3 L 2 Estimate on Stationary Linearized Boltzmann Equation 10 3.1 Construction of Solution for Damping Transport Equation . . . . . . 10 3.2 Construction of Solution for the Equation with Cut-off Linearized Boltzmann Operator . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.3 Key Estimate for L 2 Estimate . . . . . . . . . . . . . . . . . . . . . . 14 3.4 Proof of the L 2 Estimate Theorem . . . . . . . . . . . . . . . . . . . 20 4 L ∞ Estimate on Stationary Linearized Boltzmann Equation 22 4.1 Estimate on Integration on Stochastic Cycles . . . . . . . . . . . . . . 23 4.2 Iteration Scheme for L ∞ Case . . . . . . . . . . . . . . . . . . . . . . 25 4.3 Key Estimate for L ∞ Case . . . . . . . . . . . . . . . . . . . . . . . . 27 4.4 Proof of the L ∞ Estimate Theorem . . . . . . . . . . . . . . . . . . . 33 5 Existence and L ∞ Estimate for Non-isothermal Boundary 38 5.1 Iteration for Non-isothermal Boundary . . . . . . . . . . . . . . . . . 38 5.2 Proof of the Main Theorem . . . . . . . . . . . . . . . . . . . . . . . 38 6 Conclusion 42 Reference 43 | |
| dc.language.iso | en | |
| dc.subject | 波茲曼方程 | zh_TW |
| dc.subject | 擴散反射邊界條件 | zh_TW |
| dc.subject | 非恆溫邊界 | zh_TW |
| dc.subject | 穩態問題 | zh_TW |
| dc.subject | 線性化波茲曼方程 | zh_TW |
| dc.subject | Boltzmann Equation | en |
| dc.subject | Diffuse Reflection Boundary Condition | en |
| dc.subject | Non-isothermal Boundary | en |
| dc.subject | Steady Problem | en |
| dc.subject | Linearized Boltzmann Equation | en |
| dc.title | 穩態波茲曼方程在擴散反射邊界條件下解的存在性 | zh_TW |
| dc.title | Existence of Solution for Stationary Boltzmann Equation with Diffuse Reflection Boundary Condition | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 108-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 夏俊雄(Chun-Hsiung Hsia),陳俊全(Chiun-Chuan Chen) | |
| dc.subject.keyword | 波茲曼方程,擴散反射邊界條件,非恆溫邊界,穩態問題,線性化波茲曼方程, | zh_TW |
| dc.subject.keyword | Boltzmann Equation,Diffuse Reflection Boundary Condition,Non-isothermal Boundary,Steady Problem,Linearized Boltzmann Equation, | en |
| dc.relation.page | 43 | |
| dc.identifier.doi | 10.6342/NTU202001493 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2020-08-19 | |
| 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 | |
文件中的檔案：
| 檔案 | 大小 | 格式 | |
|---|---|---|---|
| U0001-1407202002121500.pdf 未授權公開取用 | 1.75 MB | Adobe PDF |
系統中的文件，除了特別指名其著作權條款之外，均受到著作權保護，並且保留所有的權利。