請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/86530完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 夏俊雄(Chun-Hsiung Hsia) | |
| dc.contributor.author | Jin-Zhi Phoong | en |
| dc.contributor.author | 馮晉知 | zh_TW |
| dc.date.accessioned | 2023-03-20T00:01:22Z | - |
| dc.date.copyright | 2022-09-07 | |
| dc.date.issued | 2022 | |
| dc.date.submitted | 2022-08-15 | |
| dc.identifier.citation | [1] R. Alexandre, Y. Morimoto, S. Ukai, C.-J. Xu, and T. Yang. The Boltzmann equation without angular cutoff in the whole space: Qualitative properties of solutions. Archive for Rational Mechanics and Analysis, 202(2):599–661, Jun 2011. [2] C. Bardos, R. E. Caflisch, and B. Nicolaenko. The Milne and Kramers problems for the Boltzmann equation of a hard sphere gas. Communications on pure and applied mathematics, 39(3):323–352, 1986. [3] L. Boltzmann. Weitere Studien über das Wärmegleichgewicht unter Gasmolekülen. k. und k. Hof- und Staatsdr., 1872. [4] C. Cercignani. Theory and application of the Boltzmann equation. Scottish Academic Press, 1975. [5] C. Cercignani et al. Mathematical methods in kinetic theory, volume 1. Springer, 1969. [6] I.-K. Chen. Boundary singularity of moments for the linearized Boltzmann equation. Journal of Statistical Physics, 153(1):93–118, 2013. [7] I.-K. Chen and C.-H. Hsia. Singularity of macroscopic variables near boundary for gases with cutoff hard potential. SIAM Journal on Mathematical Analysis, 47(6):4332–4349, 2015. [8] I.-K. Chen, T.-P. Liu, and S. Takata. Boundary singularity for thermal transpiration problem of the linearized Boltzmann equation. Archive for Rational Mechanics and Analysis, 212(2):575–595, 2014. [9] C. R. E. The Boltzmann equation with a soft potential. I. Comm. Math. Phys, 74:71– 95, 1980. [10] G. F. and P. F. Stationary solutions of the linearized Boltzmann equation in a halfsphere. Math. Methods Appl. Sci, 11:483–502, 1989. [11] Y.-H. Huang. Boundary singularity of macroscopic variables for linearized Boltzmann equation with cutoff soft potential. 2020. [12] S. R. M. Optimal time decay of the non cut-off Boltzmann equation in the whole space. Kinet. Relat. Models, 5:583–613, 2012. [13] Y. Onishi and Y. Sone. Kinetic theory of slightly strong evaporation and condensation– hydrodynamic equation and slip boundary condition for finite reynolds number– . Journal of the Physical Society of Japan, 47(5):1676–1685, 1979. [14] L. S. and Y. X. The initial boundary value problem for the Boltzmann equation with soft potential. Arch. Ration. Mech. Anal., 223:463–541, 2017. [15] U. S. and A. K. On the Cauchy problem of the Boltzmann equation with a soft potential. Publ. Res. Inst. Math. Sci., 11:477–519, 1982. [16] Y. Sone. Kinetic theory analysis of linearized Rayleigh problem. Journal of the Physical Society of Japan, 19(8):1463–1473, 1964. [17] Y. Sone. Effect of sudden change of wall temperature in rarefied gas. Journal of the Physical Society of Japan, 20(2):222–229, 1965. [18] Y. Sone. Kinetic theory of evaporation and condensation –linear and nonlinear problems–. Journal of the Physical Society of Japan, 45(1):315–320, 1978. [19] G. Y. and S. R. M. Exponential decay for soft potentials near Maxwellian. Arch. Ration. Mech. Anal., 187:287–339, 2008. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/86530 | - |
| dc.description.abstract | 波茲曼方程是描述熱力學系統演化的重要數學模型。數學家已將其廣泛應用在各個科學領域，並對其進行了許多的研究。在本文中，我們回顧了波茲曼方程碰撞算子的性質。我們主要關注於 Milne 和 Kramers 問題的解的存在性，唯一性和漸近行為。我們也介紹近期線性波茲曼方程的宏觀變量的邊界奇點方面的工作。 | zh_TW |
| dc.description.abstract | The Boltzmann Equation is an important mathematical model that describes the evolution of a thermodynamic system. It has been studied and applied in various scientific areas. In this article, we review the properties of collision operator of Boltzmann equation. We will focus mainly on the well-posedness and the asymptotic behaviour of the Milne and Kramers problem as well as the recent work in the boundary singularity of macroscopic variables for linearized Boltzmann equation. | en |
| dc.description.provenance | Made available in DSpace on 2023-03-20T00:01:22Z (GMT). No. of bitstreams: 1 U0001-1108202213214900.pdf: 509872 bytes, checksum: 38c78b589a9dade704a9e3ae5a4ed104 (MD5) Previous issue date: 2022 | en |
| dc.description.tableofcontents | Verification Letter from the Oral Examination Committee i Acknowledgements iii 摘要 v Abstract vii Contents ix Chapter 1 Introduction 1 Chapter 2 The Milne Problem 7 Chapter 3 The Kramers Problem 31 Chapter 4 Boundary singularity 37 Chapter 5 Conclusion and Challenges 55 References 57 | |
| dc.language.iso | en | |
| dc.subject | 偏微分方程 | zh_TW |
| dc.subject | 波茲曼方程 | zh_TW |
| dc.subject | 邊界奇點 | zh_TW |
| dc.subject | 偏微分方程 | zh_TW |
| dc.subject | 波茲曼方程 | zh_TW |
| dc.subject | 邊界奇點 | zh_TW |
| dc.subject | Partial Differential Equations | en |
| dc.subject | Partial Differential Equations | en |
| dc.subject | Boltzmann Equation | en |
| dc.subject | Boundary Singularities | en |
| dc.subject | Boltzmann Equation | en |
| dc.subject | Boundary Singularities | en |
| dc.title | 波茲曼方程及其邊界奇點綜述 | zh_TW |
| dc.title | A review on the Boltzmann equation and its boundary singularities | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 110-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 陳逸昆(I-Kun Chen),吳恭儉(Kung-Chien Wu) | |
| dc.subject.keyword | 偏微分方程,波茲曼方程,邊界奇點, | zh_TW |
| dc.subject.keyword | Partial Differential Equations,Boltzmann Equation,Boundary Singularities, | en |
| dc.relation.page | 59 | |
| dc.identifier.doi | 10.6342/NTU202202294 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2022-08-15 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| dc.date.embargo-lift | 2022-09-07 | - |
| 顯示於系所單位： | 數學系 | |
文件中的檔案：
| 檔案 | 大小 | 格式 | |
|---|---|---|---|
| U0001-1108202213214900.pdf | 497.92 kB | Adobe PDF | 檢視/開啟 |
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。