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  本文選題：未知源識別 + 不適定問題��； 參考：《蘭州理工大學》2016年碩士論文

【摘要】：未知源項識別問題是反問題研究中一類重要問題,在實際問題中有重要的應用背景,如新能源的探測、污染源的尋找,尤其在我國北部霧霾如此嚴重的今天,對引起霧霾的源頭尋找顯得尤為重要.本文將利用三種不同的正則化方法研究三個不適定問題.第二章研究了含對流項的一維熱傳導方程只含有空間變量的熱源識別反問題.在χ軸上以常速度運動著介質(zhì)的擴散以及液體的熱傳導規(guī)律都可以用含對流項的熱傳導方程表示.本文利用高斯核磨光滑正則化方法給出正則解,在先驗和后驗兩種正則化參數(shù)選取規(guī)則下,得到收斂的誤差估計.第三章和第四章研究了高維熱傳導方程未知熱源識別問題.我們主要研究了柱型區(qū)域和球型區(qū)域上的高維熱傳導方程的未知熱源識別問題.本文在后驗正則化參數(shù)選取規(guī)則下,分別利用簡化的Tikhonov正則化方法和譜截斷正則化方法,給出正則解與精確解之間H銉lder型誤差估計,并利用各種不同類型的數(shù)值例子驗證了我們方法的有效性.
[Abstract]:The problem of unknown source term identification is an important problem in the research of inverse problem. It has important application background in practical problems, such as the detection of new energy sources and the search of pollution sources, especially today when haze is so serious in the northern part of China. It is very important to find the source of haze. In this paper, three ill-posed problems are studied by using three different regularization methods. In chapter 2, the inverse problem of heat source identification for one-dimensional heat conduction equation with convection term is studied. The diffusion of the medium and the heat conduction of the liquid at constant velocity on the 蠂 axis can be expressed by the heat conduction equation with convection term. In this paper, the regular solution is obtained by using the Gao Si kernel grinding smooth regularization method, and the error estimates of convergence are obtained under the rules of selecting two regularization parameters a priori and a posteriori. In chapter 3 and chapter 4, the problem of identifying unknown heat source of high dimensional heat conduction equation is studied. In this paper, we mainly study the problem of identifying unknown heat sources for high dimensional heat conduction equations in cylindrical and spherical regions. In this paper, using the simplified Tikhonov regularization method and the spectral truncation regularization method, the H lder type error estimates between the regular solution and the exact solution are given under the rule of the selection of posterior regularization parameters. The effectiveness of our method is verified by various numerical examples.
【學位授予單位】：蘭州理工大學
【學位級別】：碩士
【學位授予年份】：2016
【分類號】：O241.82

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本文編號：2096624