臺灣博碩士論文加值系統

在這篇論文中,我們假設函數Fi是黏滯型守恆律方程的一個解,且解的形式為黏滯型的震波。我們關心這樣的方程在Fi附近解的行為以及穩定性。這裡我們會介紹一個方法為T-C Scheme 它是用來建造對Fi線性化過後方程的解,並且對其解做估計來判斷原方程的穩定性,這篇文章只探討穿越波部分的估計。

Assume Fi is a viscous shock profile of the viscous hyperbolic conservation laws. We are concerned with the stability and the solution structure for the initial value problem of the viscous hyperbolic conservation laws around the viscous shock wave Fi. The T-C scheme is used to estimate the solution of the linearized equations around viscous shock profile Fi. The detail proofs for the transversal wave operator of the T-C scheme are given in this thesis.

1 Introduction… p2
2 The T-C scheme… p3
2.1 Green’s functions for the linearized equation around constant states . . . p3
2.2 T-C scheme operators . . . p5
2.2.1 Approximated solution operator. . . . p5
2.2.2 Error series operator and transversal wave operator. . . p6
2.2.3 Wave front operator. . . . p7
2.2.4 Compressive wave operator. . . . p8
2.2.5 T-C scheme . . . p9
3 Estimates on the transversal operator. p9
3.1 Main result . . . p9
3.2 Preparation for estimates. . . . p10
3.3 Error series operator. . . p12
3.4 Transversal wave operator. . . p20

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