中文摘要

本文主要在探討核子反應中的中子運輸方程，此運輸現象可以用一個積分微分方程式的初始-邊界值問題來描述。這個方程式和接大部分的數學問題一樣，是屬於不可能精確求解的方程，但是我們可以免定義起始的上，下解，然後用雙邊疊代過程，分別從上方和下方單調地逼近於方程式的未知解。一般的疊代法適用於方程式本身具有某種單調性質，但實際上很多問題往往不具有這種單調性。解決這類問題，可建議用混合單調法-就是將方程式的相應算子擴增為兩個變量，它對於某個變量為單調非降，而對於另一個變量為單調非增，當這兩個變量相等時即回復到原來的算子。本文即利用混合單調法，結合相對應的雙邊不等式，討論中子運輸方程的存在性，唯一性，及是在定性，並且得到-建設性的疊代過程，可建造出單調序列分別從上方反下方逼迫方程式的唯一解。同時在疊代過程中的每一步驟都指出方程式解的分布區域，而且提供序列逼進誤差的一種方使的後驗估計。

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