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Student Number 962201032 Author Cheng-Fang Su(蘇承芳) Author's Email Address No Public. Statistics This thesis had been viewed 1299 times. Download 578 times. Department Mathematics Year 2008 Semester 2 Degree Master Type of Document Master's Thesis Language English Title Inner solutions for the viscous shock profiles of compressible Euler equations in a variable area duct Date of Defense 2009-05-15 Page Count 27 Keyword compressible Euler equations conservation laws inner solutions outer solutions singular perturbation viscous shock profiles Abstract In this paper we consider the viscous compressible Euler equations in a variable area duct. By the technique of asymptotic expansions in singular perturbations, we study the inner solutions of the viscous shock profiles. The equations for inner solutions with respect to the power of viscous constant are derived. We show that the equations of inner solutions of O(1) and O(ε) can be modified to the scalar integro-differential equations. The existence and uniqueness of solutions for such two point boundary value problems are established by contraction mapping principle. Table of Content 中文摘要 --i

英文摘要 --ii

致謝 --iii

Contents --v

List of Figures --vi

Abstract --1

1 Introduction --2

2 Derivation of Equations for Inner Solutions --4

3 Equations of Traveling Waves and Integro-differential Systems --10

4 Existence and uniqueness of Solution to the Two Point Boundary Value Problem --15

4.1 Profiles of Traveling Waves --15

4.2 Existence and uniqueness of Solutions to the Two Point Boundary Value Problem of integro-differential Equations --18

References --26Reference [1] C. M. Dafermos, Hyperbolic Conservation Laws in Continuum Physics, 2nd edition. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 325. Springer-Verlag, Berlin, 2005.

[2] J. Glimm, Solutions in the large for nonlinear hyperbolic systems of equations, Comm. Pure Appl. Math. 18 (1965), pp. 697-715.

[3] Jonathan Goodman, Zhouping Xin, Viscous Limits for Piecewise Smooth Solutions to System of Conservation Laws, Arch. Rational Mech. Anal. 121 (1992), pp. 235-265.

[4] J. M. Hong, An extension of Glimm's method to inhomogeneous strictly hyperbolic systems of conservation laws by ``weaker than weak' solutions of the Riemann problem, J. Diff. Equ. 222 (2006), pp. 515-549.

[5] J. M. Hong, C. H. Hsu, Y. C. Su, Global solutions for initial-boundary value problem of quasilinear wave equations, J. Diff. Equ. 245 (2008), pp. 223-248.

[6] P. D. Lax, Hyperbolic system of conservation laws, II, Comm. Pure Appl. Math. 10 (1957), pp. 537-566.

[7] J. Smoller, Shock Waves and Reaction Diffusion Equations, Springer-Verlag, New York, Berlin (1983).

[8] Wolfgang Walter, Ordinary Differential Equations, Springer-Verlag, New York, Berlin (1998).

[9] B. Whitham, Linear and nonlinear waves. New York, John Wiley, 1974.

[10] S.-H. Yu, Zero-dissipation limit of solutions with shocks for systems of hyperbolic conservation laws. Arch. Rational Mech. Anal. 146 (1999), pp. 275-370.Advisor John M. Hong(洪盟凱)

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962201032.pdf Date of Submission 2009-05-23

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