政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/60082
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    题名: 波茲曼方程式柔和解的存在性
    Existence result of mild solution of Boltzmann equation
    作者: 魏照誠
    Chao-Cheng Wei
    贡献者: 李明融
    魏照誠
    Chao-Cheng Wei
    关键词: 波茲曼方程
    柔和解的存在性
    均勻穩定性
    日期: 2009
    上传时间: 2013-09-04 15:15:35 (UTC+8)
    摘要: 我們利用Banach固定點定理證明了波茲曼方程式的柔和解在一個加權魯貝格空間上的存在性，並證明其解在如此的範數下之均勻穩定性。
    關鍵詞: 波茲曼方程，馬氏分佈函數，柔和解的存在性，均勻穩定。
    In this thesis, we consider the initial-value problem for the Boltzmann equation.We prove that the existence of mild solution in the weighted Lebesgue space by using Banach`s fixed point theorem, and that the uniform stability of solution with respect to the weighted norm.
    Key words: Boltzmann equation, Maxwellian, existence of mild solutions, uniform stability.
    參考文獻: @BOOK{Marsden,
    title = {A Mathematical Introduction to Fluid Mechanics},
    publisher = {Springer},
    year = {1992},
    editor = {3rd},
    author = {A.J.Chorin, J.E.Marsden},
    owner = {FUJITSU},
    timestamp = {2010.03.21}
    }

    @BOOK{Serge,
    title = {Hyperbolic Patial Differential Equations},
    publisher = {Springer},
    year = {2009},
    author = {Serge Alinhac},
    owner = {FUJITSU},
    timestamp = {2010.03.21}
    }

    @BOOK{Bird,
    title = {Molecular Gas Dynamics and the Direct simulation of Gas Flows},
    publisher = {Oxfold},
    year = {1994},
    author = {G.A. Bird},
    owner = {FUJITSU},
    timestamp = {2010.03.21}
    }

    @BOOK{Evans,
    title = {Partial Differential Equations},
    publisher = {American Mathematical Society},
    year = {1998},
    author = {Lawrence C.Evans},
    owner = {FUJITSU},
    timestamp = {2010.03.20}
    }

    @BOOK{Mario,
    title = {The Mathematical Theory of Dilute Gases},
    publisher = {Springer},
    year = {1994},
    author = {Carlo Cercignani, Reinhard llner, Mario Pulvirenti},
    owner = {FUJITSU},
    timestamp = {2010.03.20}
    }

    @BOOK{Carlo,
    title = {The Boltzmann Equation and Its Applications},
    publisher = {Springer},
    year = {1988},
    author = {Carlo Cercignani},
    owner = {FUJITSU},
    timestamp = {2010.03.20}
    }

    @ARTICLE{Hilbert,
    author = {D.Hilbert},
    title = {Begr\\"{u}ndung der Kinetischen Gastheorie},
    journal = {Mathematische Annalen 72},
    year = {1916/1917},
    pages = {562-577},
    owner = {FUJITSU},
    timestamp = {2010.04.29}
    }

    @MISC{Diperna,
    author = {R.J. Diperna and P.L. Lions},
    title = {On the {C}auchy problem for {B}oltzmann equation: {G}lobal existence
    and weak stability},
    howpublished = {Ann. of Math. 130},
    year = {1989},
    note = {pp. 321–366},
    owner = {FUJITSU},
    timestamp = {2010.04.09}
    }

    @MISC{Duan,
    author = {Renjun Duan},
    title = {On the {C}auchy problem for the {B}oltzmann equation in the whole
    space: {G}lobal existence and uniform stability in ${L}^2_{\\xi}({H}^{N}_{x})$},
    howpublished = {Journal of Differential Equations Volume 244, Issue 12},
    month = {15 June},
    year = {2008},
    owner = {FUJITSU},
    timestamp = {2010.04.09}
    }

    @BOOK{Evans,
    title = {Partial Differential Equations},
    publisher = {Providence, R.I. : American Mathematical Society},
    year = {1998},
    author = {Lawrence C. Evans},
    owner = {FUJITSU},
    timestamp = {2010.04.06}
    }

    @MISC{Guo,
    author = {Y. Guo},
    title = {The {B}oltzmann equation in the whole space},
    howpublished = {Indiana Univ. Math. J. 53},
    year = {2004},
    note = {pp. 1081–1094},
    owner = {FUJITSU},
    timestamp = {2010.04.09}
    }

    @MISC{Guo3,
    author = {Y. Guo},
    title = {The {V}lasov - {M}axwell - {B}oltzmann system near {M}axwellians},
    howpublished = {, Invent. Math. 153},
    year = {2003},
    note = {pp. 593–630},
    owner = {FUJITSU},
    timestamp = {2010.04.09}
    }

    @MISC{Guo5,
    author = {Y. Guo},
    title = {Classical solutions to the {B}oltzmann equation for molecules with
    an angular cutoff},
    howpublished = {Arch. Ration. Mech. Anal. 169},
    year = {2003},
    note = {pp. 305–353},
    owner = {FUJITSU},
    timestamp = {2010.04.09}
    }

    @MISC{Guo2,
    author = {Y. Guo},
    title = {The {L}andau equation in a periodic box},
    howpublished = {Comm. Math. Phys. 231},
    year = {2002},
    note = {pp. 391–434},
    owner = {FUJITSU},
    timestamp = {2010.04.09}
    }

    @MISC{Guo4,
    author = {Y. Guo},
    title = {The {V}lasov -{P}oisson-{B}oltzmann system near {M}axwellians},
    howpublished = {Comm. Pure Appl. Math. 55 (9)},
    year = {2002},
    note = {pp. 1104–1135},
    owner = {FUJITSU},
    timestamp = {2010.04.09}
    }

    @ARTICLE{Grad,
    author = {H.Grad},
    title = {Asymptotic equivalence of the {N}avier-{S}tokes and nonlinear {B}oltzmann
    equations},
    journal = {Proc.Symp.Appl.Math. 17},
    year = {1965},
    pages = {p.154-183},
    owner = {FUJITSU},
    timestamp = {2010.04.11}
    }

    @MISC{Yu2,
    author = {T.-P. Liu and S.-H. Yu},
    title = {Green`s function of {B}oltzmann equation, 3-{D} waves},
    howpublished = {Bull. Inst. Math. Acad. Sin. (N.S.) 1},
    year = {2006},
    note = {pp. 1–78},
    owner = {FUJITSU},
    timestamp = {2010.04.09}
    }

    @MISC{Liu2,
    author = {T.-P. Liu and S.-H. Yu},
    title = {Boltzmann equation: {M}icro -{M}acro decompositions and positivity
    of shock profiles},
    howpublished = {Comm. Math. Phys. 246 (1)},
    year = {2004},
    note = {pp. 133–179.},
    owner = {FUJITSU},
    timestamp = {2010.04.09}
    }

    @MISC{Nishida,
    author = {T. Nishida and K. Imai},
    title = {Global solutions to the initial value problem for the nonlinear {B}oltzmann
    equation},
    howpublished = {Publ. Res. Inst. Math. Sci. 12},
    year = {1976/77},
    note = {pp. 229–239},
    owner = {FUJITSU},
    timestamp = {2010.04.09}
    }

    @MISC{Shizuta,
    author = {Y. Shizuta},
    title = {On the classical solutions of the {B}oltzmann equation},
    howpublished = {Comm. Pure Appl. Math. 36},
    year = {1983},
    note = {pp. 705–754},
    owner = {FUJITSU},
    timestamp = {2010.04.09}
    }

    @BOOK{Boltzmann,
    title = {Lectures On Gas Theory},
    publisher = {Dover Publications},
    year = {1995},
    author = {Ludwig Boltzmann ; translated by Stephen G. Brush},
    owner = {FUJITSU},
    timestamp = {2010.03.21}
    }

    @BOOK{Chapman,
    title = {The Mathematical Theory of Non-Uniform Gases},
    publisher = {Cambridge University Press},
    year = {1970},
    editor = {3rd},
    author = {Sydney Chapman, T.G.Cowling},
    owner = {FUJITSU},
    timestamp = {2010.03.21}
    }

    @MISC{Liu,
    author = {T.-P. Liu, T. Yang and S.-H. Yu},
    title = {Energy method for the {B}oltzmann equation},
    howpublished = {Phys. D 188 (3–4)},
    year = {2004},
    note = {pp. 178–192},
    owner = {FUJITSU},
    timestamp = {2010.04.09}
    }

    @MISC{Yu,
    author = {T.-P. Liu, T. Yang, S.-H. Yu and H. Zhao},
    title = {Nonlinear stability of rarefaction waves for {B}oltzmann equation},
    howpublished = {Arch. Ration. Mech. Anal. 181 (2)},
    year = {2006},
    note = {pp. 333–371},
    owner = {FUJITSU},
    timestamp = {2010.04.09}
    }

    @ARTICLE{Carleman,
    author = {T.S.Carleman},
    title = {Sur la th\\`{e}orie de l`\\`{e}quation int\\`{e}gro-differentielle de
    {B}oltzmann},
    journal = {Acta.Math,60},
    year = {1932},
    pages = {p.91-146},
    owner = {FUJITSU},
    timestamp = {2010.04.10}
    }

    @MISC{Ukai,
    author = {S. Ukai},
    title = {On the existence of global solutions of mixed problem for non-linear
    {B}oltzmann equation},
    howpublished = {Proc. Japan Acad. 50},
    year = {1974},
    note = {pp. 179–184},
    owner = {FUJITSU},
    timestamp = {2010.04.09}
    }

    @MISC{Yang2,
    author = {S. Ukai and T. Yang},
    title = {The {B}oltzmann equation in the space ${L}^2\\cap {L}^{\\infty}_{\\beta}$
    : Global and time-periodic solutions},
    howpublished = {Anal. Appl. 4},
    year = {2006},
    note = {pp. 263–310},
    owner = {FUJITSU},
    timestamp = {2010.04.09}
    }

    @BOOK{Yang3,
    title = {Mathematical Theory of Boltzmann Equation},
    publisher = {Liu Bie Ju Centre for Mathematical Sciences, Lecture Notes Series,
    No. 8},
    year = {2006},
    author = {S. Ukai and T. Yang},
    owner = {FUJITSU},
    timestamp = {2010.05.15}
    }

    @MISC{Yang,
    author = {T. Yang and H.-J. Zhao},
    title = {A new energy method for the {B}oltzmann equation},
    howpublished = {J. Math. Phys. 47},
    year = {2006},
    note = {p. 053301},
    owner = {FUJITSU},
    timestamp = {2010.04.09}
    }

    @ARTICLE{Yu3,
    author = {Shih-Hsien Yu},
    title = {Hydrodynamic limits with Shock Waves of the {B}oltzmann equation},
    journal = {Commun. Pur. Appl. Math, 58},
    year = {2005},
    pages = {409-443},
    owner = {FUJITSU},
    timestamp = {2010.05.02}
    }
    描述: 碩士
    國立政治大學
    應用數學研究所
    97751004
    98
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    数据类型: thesis
    显示于类别:[應用數學系] 學位論文

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