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理學院
數學系
學位論文
學位論文
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http://rportal.lib.ntnu.edu.tw/handle/20.500.12235/73901
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search.filters.author.凌家東
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search.filters.author.Chia-Tung Ling
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search.filters.subject.complex-valued heat equation
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search.filters.subject.殆核解
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拋物型問題的奇異點研究
(
2012
)
凌家東
;
Chia-Tung Ling
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在本論文中,我們要討論從二個拋物型方程得到的二種不同類型的奇異點問題。本論文分為二個部份, 在第一部份中,我們考慮具有快速擴散項與強吸收非線性項之方程的殆核問題。首先,我們證明解殆核的速度是非自我相似的。接著,在考慮重新縮放的解與殆核最終在單點發生的狀態下,我們得到一些更精確的估計。 在第二部份中,我們探討一個由複數取值的熱方程得到的柯西問題,而其中的非線性項是倒數型的。首先,我們提供了一些解的全局存在性與消失性的判斷準則。接下來,我們證明當初始值為漸近常數時,解是否會在無窮遠處消失或是在任意的時間內全局存在,均依賴於初始值的漸近極限值。
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