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研究生:陳俊傑
研究生(外文):Chen,Jun-Jie
論文名稱:Survey On The Paper " First Order Quasilinear Equations In Several Independent Variables " By S.N.Kruzkov
論文名稱(外文):Survey On The Paper " First Order Quasilinear Equations In Several Independent Variables " By S.N.Kruzkov
指導教授:徐淑裕
指導教授(外文):Hsu,Shu-Yu
口試委員:潘志祥吳進通
口試委員(外文):Poon,Chi-CheungWu,Chin-Tung
口試日期:2016-06-28
學位類別:碩士
校院名稱:國立中正大學
系所名稱:數學系應用數學研究所
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:2016
畢業學年度:104
語文別:英文
論文頁數:36
外文關鍵詞:Kruzkov
相關次數:
  • 被引用被引用:0
  • 點閱點閱:160
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  • 下載下載:8
  • 收藏至我的研究室書目清單書目收藏:0
In this thesis I will survey a theory by S.N.Kruzkov on the
existence and uniqueness of bounded generalized solution
of Cauchy's problem. We define the generalized
solution and prove existence, uniqueness and stability
theorems for this solution. Vanishing viscosity method is
need to prove existence of solution of the above equation.

S.N.Kruzkov
P.3 Introduction
P.4 Statement Of Cauchy's Problem (1.1), (1.2); Some Notation And Preliminary Observations
P.9 Uniqueness Of The Generalized Solution Of Problem (1.1), (1.2); Stability With Respect To The Initial Condition
P.19 Existence Of The Generalized Solution Of Problem (1.1), (1.2)
P.35 References
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Englewood Cliffs, N. J., 1964; Russian transl., "Mir", Moscow, 1968. MR 31
#6062.
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ables, Mat. Sbornik Tom 81 (123) (1970), no. 2 = Math. USSR Sbornik vol.
10 (1970), no. 2.
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Soviet Math. Dokl. 10 (1969), 785-788. MR 40 #3046.
[11] S. N. Kruzkov, Methods for constructing generalized solutions for the Cauthy
problem for a quasilinear equation of the first order, Uspehi Mat. Nauk 20
(1965), no. 6 (126), 112-118. (Russian) MR 33 #391.
[12] S. N. Kruzkov, Results on the nature of the continuity of solutions of parabolic
equations, and certain applications thereof, Mat. Zametki 6 (1969), 97-108.
(Russian) MR 40 #3073.
[13] P. D. Lax, Weak solutions of nonlinear hyperbolic equations and their
numerical computation, Comm. Pure Appl. Math. 7 (1954), 159-193. MR 16,
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[17] O. A. Oleinik, Cauchy's problem for nonlinear equations in a class of
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