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研究生:簡妟伃
研究生(外文):Yen-Yu Chien
論文名稱:擬線性拋物型方程之非線性邊界值問題的自我相似解
論文名稱(外文):Self-similar Solutions for a Quasilinear Parabolic Equation with Nonlinear Boundary Condition.
指導教授:郭忠勝
指導教授(外文):Jong-Sheng Guo
學位類別:碩士
校院名稱:國立臺灣師範大學
系所名稱:數學系
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
畢業學年度:94
語文別:英文
論文頁數:15
中文關鍵詞:擬線性拋物型方程自我相似解消失性投射法漸近行為
外文關鍵詞:quasilinear parabolic equationself-similar solutionsquenchingshooting methodasymptotic behavior
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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,我們證明了解的消失性。然後,藉研究所對應之常微分方程的初值問題,我們利用投射法證明了單調遞減全域解的存在。最後,我們分析任一單調遞減全域解的漸近行為。
In this paper, we study the self-similar solutions for a quasilinear parabolic equation with nonlinear boundary condition. We first prove that quenching always occurs. Then, by considering the initial value problem, we prove the existence of globally monotone decreasing solutions by a shooting method. Finally, we study the asymptotic behavior of any globally monotone decreasing solution.
Introduction 1
Preliminaries 3
Existence 7
Asymptotic behavior 14
Reference
[1]C.Y. Chan, Recent advances in quenching phenomena,
Proc. of Dynamic Systems and Appl. 2 (1996), 107--113.

[2]R. Ferreira, A. de Pablo, F. Quiro's, and J. D. Rossi,
Superfast quenching, Journal of Differential Equations 199 (2004) 189-209.

[3]M. Fila, J.-S. Guo, Complete blow-up and incomplete quenching for the heat equation with a nonlinear boundary condition, Nonlinear Analysis, TMA 48 (2002), 995--1002.

[4]M. Fila, H.A. Levine, Quenching on the boundary,
Nonlinear Analysis, TMA 21 (1993), 795--802.

[5]J.-S. Guo, On a quenching problem with the Robin boundary condition, Nonlinear Analysis, TMA 17 (1991), 803--809.

[6]J.-S. Guo, On the quenching rate estimate,
Quarterly of Appl. Math. 49 (1991), 747-752.

[7]J.-S. Guo, Quenching behavior for a fast diffusion equation with absorption, Dynamic Systems & Applications 4 (1995), 47--56.

[8]J.-S. Guo, Similarity solutions for a quasilinear
parabolic equation, J. Austral. Math. Soc. Ser. B 375
(1995) 253-266.

[9]J.-S. Guo, Bei Hu, Quenching profile for a quasilinear parabolic equation, Quarterly of Applied Mathematics 58 (2000), 613--626.

[10]H. Kawarada, On solutions of initial boundary value problem for u_t = u_{xx} + {1/(1-u)}, Publ. RIMS, Kyoto U. 10 (1975), pp. 729--736.

[11]H.A. Levine, The phenomenon of quenching: A survey, in
Proc. 6th Int. Conf. on Trends in the Theory and Practice of
Nonlinear Analysis, North Holland, New York, 1985, pp. 275--286.

[12]H.A. Levine, Advances in quenching,
in Proc. International Conference on Nonlinear Diffusion Equations and Their
Equilibrium States, Gregynog, Wales, August 1989
(edited by N. G. Lloyd et al.),
Birkh"auser, Boston, 1992, pp. 319--346.
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