English  |  正體中文  |  简体中文  |  Items with full text/Total items : 73032/73032 (100%)
Visitors : 23358004      Online Users : 548
RC Version 7.0 © Powered By DSPACE, MIT. Enhanced by NTU Library IR team.
Scope Tips:
  • please add "double quotation mark" for query phrases to get precise results
  • please goto advance search for comprehansive author search
  • Adv. Search
    HomeLoginUploadHelpAboutAdminister Goto mobile version

    Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/65877

    Title: 探討源自於隨機最佳化控制問題之偏微分方程與其相關應用;Solutions of Partial Differential Equations Arising from Stochastic Optimal Control Problems and Applications
    Authors: 吳彥霖;Wu,Yen-Lin
    Contributors: 數學系
    Keywords: 二階橢圓偏微分方程;隨機最佳化控制問題;存在性;唯一性;Partial Differential Equations;Stochastic Optimal Control Problems;Existence;Uniqueness
    Date: 2014-07-07
    Issue Date: 2014-10-15 17:16:38 (UTC+8)
    Publisher: 國立中央大學
    Abstract: 本論文主要探討三種不同型態之二階非線性橢圓偏微分方程式,其解的存在性、唯一性與結構性之相關定性分析及研究。第一部分中,我們考慮一個與隨機最佳化控制問題(stochastic optimal control problem)相關之方程,其具所謂『梯度約束方程式(gradient constraint equation)』之型態;在其非線性項更加弱化的條件下,我們證得其正解之存在性與唯一性。第二部分中,我們考慮一個座落於雙曲空間(hyperbolic space)中之半線性橢圓偏微分方程;研究其正奇異解在原點的漸近行為並且提供此正奇異解之存在性與唯一性;除此之外,我們透過『Pohozaev恆等式』了解其他不同型態解之特性,藉此進一步獲得某些特定型態解之不存在性。最後,在第三部分中我們考慮所謂的『Hardy-Sobolev方程』;在不同的指數條件下,我們研究其解的存在性、唯一性以及原點或無窮遠之行為。;This dissertation is concerned with studying some second order elliptic partial differential equations. We are devote to establishing some qualitative properties of solutions, including existence, uniqueness and structure of solutions to three specific types of nonlinear elliptic equations. In Part 1, we study a gradient constraint equation which is related to a stochastic optimal control problem. We offer the existence and uniqueness of positive radial solutions with certain behavior under weaker conditions on nonlinearity. In Part 2, we consider a semilinear elliptic equation on the hyperbolic space. The asymptotic behavior, existence and uniqueness of positive singular solutions at the origin are proved. In addition, we discuss the structure of solutions of various types via the Pohozaev identity. Finally, in our last chapter, we deal with the Hardy-Sobolev equations and investigate behaviors, existence and uniqueness of solutions for different exponents.
    Appears in Collections:[數學研究所] 博碩士論文

    Files in This Item:

    File Description SizeFormat

    All items in NCUIR are protected by copyright, with all rights reserved.

    社群 sharing

    ::: Copyright National Central University. | 國立中央大學圖書館版權所有 | 收藏本站 | 設為首頁 | 最佳瀏覽畫面: 1024*768 | 建站日期:8-24-2009 :::
    DSpace Software Copyright © 2002-2004  MIT &  Hewlett-Packard  /   Enhanced by   NTU Library IR team Copyright ©   - Feedback  - 隱私權政策聲明