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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/90007完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳逸昆 | zh_TW |
| dc.contributor.advisor | I-Kun Chen | en |
| dc.contributor.author | 林浚騰 | zh_TW |
| dc.contributor.author | Jun-Teng Lin | en |
| dc.date.accessioned | 2023-09-22T17:01:57Z | - |
| dc.date.available | 2023-11-09 | - |
| dc.date.copyright | 2023-09-22 | - |
| dc.date.issued | 2023 | - |
| dc.date.submitted | 2023-08-09 | - |
| dc.identifier.citation | [1]R. Alonso and E. Carneiro, Estimates for the Boltzmann collision operator via radial symmetry and Fourier transform, Adv. Math., 223 (2010), pp. 511-528.
[2]R. Alonso, E. Carneiro and I.M. Gamba, Convolution inequalities for the Boltzmann collision operator, Comm. Math. Physics, 298 (2010), pp. 293-322. [3]R. Alonso and I.M. Gamba, Gain of integrability for the Boltzmann collisional operator, Kinet. Relat. Models, 4 (2011), pp. 41-51. [4]Do Carmo, Differential Geometry of Curves and Surfaces (1976), pp. 232 [5]R. Duduchava, R. Kirsch, and S. Rjasanow, On estimates of the Boltzmann collision operator with cutoff, J. Math. Fluid Mech., 8 (2006), pp. 242-266. [6]T. Gustsfsson, Global Lp properties for the spatially homogenous Boltzmann equation, Arch. Rational Mech. Anal., 103 (1988), pp. 1-38. [7]P.R. Halmos and V.S. Sunder, Bounded integral operators on $L^2$ spaces, vol 96, theorem 5.2 [8]Y.S. Han and J. Zhang, Cotlar-Stein Lemma and the Tb Theorem, vol 129 (2001), pp. 1697-1698. [9]Jin-Cheng Jiang, Sharp Regularizing Estimates for the Gain Term of the Boltzmann Collision Operator. [10]P.L. Lions, Compactness in Boltzmann's equation via Fourier integral operators and applications, 34 (1994), pp. 391-427, pp. 429-461. [11]J.P. McClure and R. Wong, Multidimensional stationary phase approximation: boundary stationary point, Journal of Computational and Applied Mathematics 30 (1990), pp. 213. [12]L. Rodino, M.W.Wong and H. Zhu, Pseudo-Differential Operators: Analysis, Applications and Computations, vol 203, pp. 35. [13]B.W. Schulze and M.W. Wong, Pseudo-Differential Operators: Complex Analysis and Partial Differential Equations, vol 205 (2008), pp. 51. [14]B. Wennberg, Regularity in the Boltzmann equation and the radon transfrom, Comm. Partial Differential Equations, 19 (1994), pp. 2057-2074. | - |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/90007 | - |
| dc.description.abstract | 這篇論文主要是探討江金城教授研究的波茲曼碰撞算子，其中有用到穩定相態公式的逼近，進而解釋一些特定算子在各個區域上，範數(norm)都是有界的。 | zh_TW |
| dc.description.abstract | In this thesis, we review some regularity results for the gain term of the Boltzmann collision operator obtained by Jin-Cheng Jiang. In addition to the stationary phase, the specific decomposition of operators is the key element in the research. | en |
| dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2023-09-22T17:01:57Z No. of bitstreams: 0 | en |
| dc.description.provenance | Made available in DSpace on 2023-09-22T17:01:57Z (GMT). No. of bitstreams: 0 | en |
| dc.description.tableofcontents | 1.Introduction 1
2.Definitions and Notations 2 3.Radon Transform 3 4.Dyadic Partition of Unity 8 5.Estimate on the Region A 8 6.Estimate on the Region B and C 25 References 27 | - |
| dc.language.iso | en | - |
| dc.subject | Cotlar-Stein引理 | zh_TW |
| dc.subject | Schur引理 | zh_TW |
| dc.subject | 區域分割 | zh_TW |
| dc.subject | 波茲曼碰撞算子 | zh_TW |
| dc.subject | Radon轉換 | zh_TW |
| dc.subject | 穩定相態公式 | zh_TW |
| dc.subject | Radon Transform | en |
| dc.subject | Stationary Phase Formula | en |
| dc.subject | Schur Test Lemma | en |
| dc.subject | Dyadic Partition of Unity | en |
| dc.subject | Boltzmann Collision Operator | en |
| dc.subject | Cotlar-Stein Lemma | en |
| dc.title | 波茲曼碰撞算子的增益項之平滑性 | zh_TW |
| dc.title | On the Regularity for the Gain Term of the Boltzmann Collision Operator | en |
| dc.type | Thesis | - |
| dc.date.schoolyear | 111-2 | - |
| dc.description.degree | 碩士 | - |
| dc.contributor.oralexamcommittee | 陳俊全;江金城 | zh_TW |
| dc.contributor.oralexamcommittee | Chiun-Chuan Chen;Jin-Cheng Jiang | en |
| dc.subject.keyword | 波茲曼碰撞算子,Radon轉換,區域分割,穩定相態公式,Schur引理,Cotlar-Stein引理, | zh_TW |
| dc.subject.keyword | Boltzmann Collision Operator,Radon Transform,Dyadic Partition of Unity,Stationary Phase Formula,Schur Test Lemma,Cotlar-Stein Lemma, | en |
| dc.relation.page | 27 | - |
| dc.identifier.doi | 10.6342/NTU202302712 | - |
| dc.rights.note | 同意授權(限校園內公開) | - |
| dc.date.accepted | 2023-08-10 | - |
| dc.contributor.author-college | 理學院 | - |
| dc.contributor.author-dept | 數學系 | - |
| 顯示於系所單位： | 數學系 | |
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