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    Please use this identifier to cite or link to this item: http://nthur.lib.nthu.edu.tw/dspace/handle/987654321/86559


    Title: 波方程上的局部適定性問題
    Authors: 卓冠宇
    Zhuo, Guan-Yu
    Description: GH02101021507
    碩士
    數學系
    Date: 2014
    Keywords: 波方程
    Wave equation
    Abstract: 本篇論文一開始會先介紹波方程和薛丁格方程上的Strichartz estimate,接著
    會運用此估計,去解決波方程上的局部適定性問題(Local well-posedness)。
    In this dissertation we discuss the Strichartz estimates on the Schrodinger
    equation, Wave equation and application of the Wave equation.
    First part we introduce some de?nitions, notations and basic theorems
    from real analysis.
    Second part we will prove the Strichartz estimates on the Schrodinger
    equation follows from Tao?s Nonlinear dispersive equations: local and global
    analysis and the Wave equation on R3. On the Wave equation, we will follow
    the proofs from Christopher D. Sogge, Lectures on nonlinear wave equations.
    The Littlewood-paley theorem plays a important role in this proof and we
    use many technique of scaling.
    Finally, we will use the Strichartz estimates on theWave equation of form
    u = juj2u;Dom(u) = R1+3
    + with initial data u(0; ) = f; @tu(0; ) = g to
    solve the existence of (weak) solutions and use same idea to get the local
    well-posedness.
    URI: http://nthur.lib.nthu.edu.tw/dspace/handle/987654321/86559
    Source: http://thesis.nthu.edu.tw/cgi-bin/gs/hugsweb.cgi?o=dnthucdr&i=sGH02101021507.id
    Appears in Collections:[數學系] 博碩士論文

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