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Student Number 952201025
Author Man-meng Io(姚文銘)
Author's Email Address ar_gold@yahoo.com
Statistics This thesis had been viewed 1161 times. Download 512 times.
Department Mathematics
Year 2007
Semester 2
Degree Master
Type of Document Master's Thesis
Language English
Title Classical Solutions to the Perturbed Riemann Problem of Scalar Resonant Balance Law
Date of Defense 2008-06-14
Page Count 24
Keyword
  • Characteristic method
  • Conservation laws
  • Lax's method
  • Nonlinear balance laws
  • Perturbed Riemann problems
  • Riemann problems
  • Abstract In this paper we study the classical solutions to the perturbed Riemann problem of some scalar nonlinear balance law in resonant case. The equation with source term is equivalent to a 2×2 nonlinear balance laws as described in [6, 7], and it is a resonant system due to the fact that the speeds of waves in the solution to this 2×2 system coincide. The characteristic method in [8] is applied to construct the classical solutions of perturbed Riemann problem. Moreover, we show that, the pointwise limit of classical solutions, which are defined as the
    measurable solutions to the corresponding Riemann problem (with singular source) of perturbed Riemann problem, are self-similar as described in [12].
    Table of Content 中文摘要 ………………………………………………………………i
    英文摘要 ………………………………………………………………ii
    Acknowledgement ………………………………………………………iii
    目錄 ……………………………………………………………………iv
    圖目錄 …………………………………………………………………v
    表目錄 ……………………………………………………………………vi
    1. Introduction …………………………………………………………2
    2. Classical solutions of perturbed Riemann problem …………5
    3. Stability of perturbed Riemann solutions …………………17
    References ………………………………………………………………23
    Reference [1] C. Dafermos, Generalized characteristics and the structure of solutions of hyperbolic conservation laws, Ind. Univ. Math. J. 26 (1977), 1097-1119.
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    [3] G. Dal Maso, P. LeFloch and F. Murat, Definition and weak stability of nonconservative products, J. Math. Pure. Appl., 74(1995), 483-548.
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    [7] J. M. Hong and B. Temple, A Bound on the Total Variation of the Conserved Quantities for Solutions of a General Resonant Nonlinear Balance Law, SIAM J. Appl. Math. 64, No 3, (2004), pp 625-640.
    [8] J. M. Hong, Y. Chang and S.-W. Chou, Generalized Solutions to the Riemann Problem of Scalar Balance Law with Singular Source Term, preprint.
    [9] E. Isaacson and B. Temple, Convergence of 2 × 2 by Godunov method for a general resonant nonlinear balance law, SIAM J. Appl. Math. 55 (1995), pp 625-640.
    [10] K. T. Joseph and P. G. LeFloch, Singular limits for the Riemann problem: general diffusion, relaxation, and boundary condition, in ” new analytical approach to multidimensional balance laws”, O. Rozanova ed., Nova Press, 2004.
    23[11] S. Kruzkov, First order quasilinear equations with several space variables, Math. USSR Sbornik 10 (1970), 217-273.
    [12] P. D. Lax, Hyperbolic system of conservation laws, II, Comm. Pure Appl. Math., 10(1957), 537-566.
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    [18] C. Sinestrari, The Riemann problem for an inhomogeneous conservation law without convexity, Siam J. Math. Anal., Vo28, No1, (1997), 109-135.
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    [20] M. Slemrod and A. Tzavaras, A limiting viscosity approach for the Riemann problem in isentropic gas dynamics, Ind. Univ. Math. J. 38 (1989), 1047-1073.
    [21] J. Smoller, Shock waves and reaction-dffusion equations, Springer, New York, 1983.
    [22] A. Tzavaras, Waves interactions and variation estimates for self-similar zero viscosity limits in systems of conservation laws, Arch. Ration. Mech. Anal., 135 (1996), 1-60.
    [23] A. Volpert, The space BV and quasilinear equations, Maths. USSR Sbornik 2 (1967), 225-267.
    Advisor
  • John M. Hong(洪盟凱)
  • Files
  • 952201025.pdf
  • approve immediately
    Date of Submission 2008-07-21

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