一個微分積分問題的解之存在與唯一性

Abstract

在本論文中,我們證明了一個微分積分問題的解之存在性與唯一性.這個問 題包含二個變數:c和.alpha.當0.ltoreq c .ltoreq 1 時,我們可以得到 一個全面且均勻有界的解.當c>1時,可以得到一個局部且均勻有界的解.並 且,當空間變數趨近無窮大時,平行板的解會收斂至半平面的最小正解. In this thesis, we examine the existence and uniqueness for the solution of a nonlinear integrodifferential initial- value problem which is induced from a "simple transport modle" in the slab geometry. Our main results contain the following: First, the existence and uniqueness of a global, uniformly bounded solution are showed for all 0.ltoreq c .ltoreq 1 and 0.lotoreq. alpha.1. Second, the existence and uniqueness of a local, uniformly bounded solution are also proved for all c>1. Third, we also find out the relationship between the solution in the half space and that of in the slab geometry.