| 姓名 |
林信宏(Shin-Hong Lin)
查詢紙本館藏 |
畢業系所 |
數學系 |
| 論文名稱 |
水文地質學的平衡模型之擴散對流反應方程
(Equilibrium Models to the Reaction-Convection-Diffusion Equations in Hydrogeology)
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| 相關論文 | |
| 檔案 |
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[Bibtex 格式]
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| 摘要(中) |
我的論文主要介紹水文地質學的平衡模型。我們先引進一些假設和符號並介紹水文地質學中的吸附運動。利用極大值原理證明方程式解的非負性，並由能量法證明解對微小攝動的穩定性。最後我們研究方程式的行進波解，證明行進波的存在性和研究不連續的行進波性質，並給出兩個例子來計算。 |
| 摘要(英) |
In this thesis we introduce the equilibrium model of hydrogeology. We give the notations and assumptions in hydrogeology and introduce the adsorption kinetics. The positive solutions of the model is studied by the maximum principle, and energy method is provided to get the stability of small perturbations. Moreover, the existence and behavior of traveling wave solutions to equilibrium model is considered. Finally, we study the discontinuous traveling waves and gives two applications. |
| 關鍵字(中) |
★ 擴散對流反應方程
★ 極大值原理
★ 行進波 |
關鍵字(英) |
★ reaction-convection-diffusion equations
★ maximum principle
★ traveling waves |
| 論文目次 |
Contents of figures…………………………………………ii
1.Introduction…………………………………………………2
2.Comparison principle and energy method………………5
3.The behavior of traveling waves solutions………… 8 |
| 參考文獻 |
[1] J.Logan, Transport modeling in hydrogeochemical systems, Springer, New York, 2001.
[2] J.Logan, An introduction to nonlinear partial differential equations, Wiley-Interscience, New York, 1994.
[3] M.P.Protter and H.F.Weinberger, Maximum principles in differential equations, Prentice-Hall, Englewood Cliffs, 1967.
[4] J. Smoller, Shock waves and reaction-diffusion equations, Springer, New York,1983. |
| 指導教授 |
洪盟凱(John M. Hong)
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審核日期 |
2008-7-2 |
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