跳到主要內容

臺灣博碩士論文加值系統

(44.210.99.209) 您好!臺灣時間:2024/04/18 16:40
字體大小: 字級放大   字級縮小   預設字形  
回查詢結果 :::

詳目顯示

我願授權國圖
: 
twitterline
研究生:林芳成
研究生(外文):Fang-Chen Lin
論文名稱(外文):Harnack Inequalities for Elliptic and Parabolic Equations
指導教授:褚孫錦
學位類別:碩士
校院名稱:國立中正大學
系所名稱:數學研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2004
畢業學年度:93
語文別:中文
論文頁數:48
外文關鍵詞:Harnack inequalities
相關次數:
  • 被引用被引用:0
  • 點閱點閱:186
  • 評分評分:
  • 下載下載:0
  • 收藏至我的研究室書目清單書目收藏:0
In this report, we shall survey seral Harnack inequalities for elliptic and parabolic equations, and derive these estimates.
Introduction 1
1 Harnack inequalities 3
1.1 Harnack inequalities for elliptic PDE . . . . . . . . . . . . . . 3
1.2 Harnack inequalities for parabolic PDE . . . . . . . . . . . . 7
2 The porous medium equation @u
@t = 4(uM) 19
2.1 M > 1 (The Migration Equation) . . . . . . . . . . . . . . . 20
2.1.1 Harnack inequality of porous medium equation with
M > 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.1.2 The migration equation . . . . . . . . . . . . . . . . . 23
2.2 M = 1 (Heat equation) . . . . . . . . . . . . . . . . . . . . . 26
2.3 M < 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3 General Harnack type inequalities 31
3.1 p-diffusion equation . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2 General prior bounds . . . . . . . . . . . . . . . . . . . . . . . 33
3.2.1 Proof of the theorem . . . . . . . . . . . . . . . . . . . 33
3.2.2 Application of the theorem . . . . . . . . . . . . . . . . 42
References
[A] D. G. Aronson, The porous medium equation, Nonliner Duffusion
Promblems (A. Fasano and M. Primicerio, eds), Lecture Notes in
Math., vol. 1224, Springer-Verlag, Berlin, 1986.
[AB] D. G. Aronson and P. Benilan, Regularite des solutions de lequation
des milineux poreux dans Rn, Acad. Sci. Paris Ser. I Math. 288(1979),
103-105.
[ABo] G. Auchmuty and D. Bao, Harnack-type inequalities for evolution
equation, A.M.S, vol. 122, no. 1, September 1994.
[BH] J.G. Berryman and C.J. Holland Stability of the separable solution
for fast diffusion, Arch. Rat. Mexh. Anal., 74(1980), 279-288.
[E] L. C. Evans, Partial differential equations, A.M.S, 1998.
[EV] J.R. Esteban and J.L. Vasquez, Regularity of nonnegative solutions
of the p-Laplacian parabolic equation, 1a Reunion Hispano-Italiana
de Analisis No linealy Matematica Applicada, 1989, 87-92.
[GT] D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations
of Second Order, Springer-Verlag Wien New York, 1993.
[Ham] R. Hamilton, Differential harnack estimates for parabolic equations,
A.M.S, 2005.
[Har] A. Harnack, Grundlagen der Theorie des Logarithmischen Potentials,
Teubner, Leipzing, 1887.
[M] J. Moser, A Harnack inequality for parabolic differential equations,
Comm. Pure. Appl. Math. 17(1964), 101-134.
[MM] M. Marcus and V.J. Mizel, Absolute continuity on tracks and mappings
of Sobolev spaces, Arch. Rational Mech. Anal., 45(1972), 294-
320.
[QF] H. Qing and L. Fanghau, Elliptic Partial differential equations,
A.M.S, 1997.
[ZR] Ya.B. Zeldovich and Yu.P. Raizer, Physics of shock-waves and hightemperature
Hydrodynamic Phenomena, Vol.II, Academic Press, New
York, 1966.
QRCODE
 
 
 
 
 
                                                                                                                                                                                                                                                                                                                                                                                                               
第一頁 上一頁 下一頁 最後一頁 top
無相關論文