一個非線性消失性問題相似解的結構性

The Structure of Self-similar Solutions for a Nonlinear Quenching Problem

姚志鴻(Chih-Hung Yao)

指導教授 ： 郭忠勝

國立臺灣師範大學/理學院/數學系/碩士(2007年)

摘要

這篇論文主要是研究擬線性拋物型方程之非線性邊界值問題的自我相似解。首先對原本的常微分方程作變數變換。然後，研究所對應之常微分方程的邊界值問題，我們利用投射法來證明自我相似解的存在性。

關鍵字

擬線性拋物型方程 ； 自我相似解 ； 投射法

並列摘要

In this paper, we study the self-similar solutions for a quasilinear parabolic eauation with nonlinear boundary condition. At first, we change of variables with respect to the original ordinary differential equation. Then, by considering the boundary value problem, we prove the existence of self-similar solutions by a shooting method.

並列關鍵字

quasilinear parabolic equation ； self-similar solutions ； shooting method

參考文獻

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