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| 研究生： |
李正昌 Cheng -Chang Lee |
|---|---|
| 論文名稱： |
具有源的快擴散方程的行波解 Traveling Wave Solutions for A Fast Diffusion Equation with Source |
| 指導教授： |
郭忠勝
Guo, Jong-Shenq |
| 學位類別： |
碩士 Master |
| 系所名稱： |
數學系 Department of Mathematics |
| 論文出版年： | 2001 |
| 畢業學年度： | 89 |
| 語文別： | 英文 |
| 論文頁數： | 29 |
| 中文關鍵詞： | 行波解 、穩定性 |
| 英文關鍵詞： | traveling wave solutions, stability |
| 論文種類： | 學術論文 |
| 相關次數： | 點閱：218 下載：3 |
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中 文 摘 要
我們要研究有源（source）的快擴散方程（fast diffusion equation）的行波解（traveling wave solutions）。我們利用 Fife和McLeod 的方法，而獲得這個方程的行波解的存在性、唯一性。然後，行波解的穩定性（stability）也就得到了。
Abstract
We study the traveling wave solutions for a fast diffusion equation with source. Using a method of Fife and McLeod, we obtain the existence and uniqueness (up to translations) of the traveling wave solution of this equation. Then the stability of the traveling wave solutions is also derived.
References
[AW] D.G. Aronson and H.F. Weinberger, Multidimensional nonlinear diffusion arising in population genetics. Adv. in Math., 30 (1978) 33-76.
[FM] P.C. Fife and J.B. McLeod, The approach of solutions of nonlinear equations to traveling front solutions, Arch. Rational Mech. Anal. 65 (1977), 335-361.
[H] Y. Hosono, Traveling wave solutions for some density dependent diffusion equations, Japan J. Appl. Math. 3 (1986), 163-196.
[K1] Ya.I. Kanel', On the stabilization of solutions of the Cauchy problem for equations arising in the theory of combustion, Mat. Sbornik 59 (1962), 245-288.
[K2] Ya.I. Kanel', On the stabilization of solutions of the equations of the theory of combustion with initial data of compact support, Mat. Sbornik 65 (1964), 398-413.
[PW] M.H. Protter and H.F. Weinberger, Maximum Principles in Differential Equations, Prentice-Hall: Englewood Cliffs, N.J. 1967.
[S1] D.H. Sattinger, Weighted norms for the stability of traveling waves, J. Differential Equations, 25 (1977), 130-144.
[S2] D.H. Sattinger, On the stability of waves of nonlinear parabolic systems, Advances in Math. 22 (1976), 312-355.