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研究生： 李育誠
Yu-cheng Lee
論文名稱： 二階非線性守恆律的整體經典解
Global Classical Solutions for the 2 × 2 Nonlinear Balance Laws
指導教授： 洪盟凱
John M. Hong
口試委員:
學位類別： 碩士
Master
系所名稱： 理學院 - 數學系
Department of Mathematics
畢業學年度： 98
語文別： 英文
論文頁數： 24
中文關鍵詞： 雙曲守恆律 、非線性守恆律 、柯西問題 、整體經典解 、特徵線法
外文關鍵詞： Nonlinear balance laws, Hyperbolic conservation laws, Characteristic method, Global classical solutions, Cauchy problem
相關次數： 點閱：15  下載：0 
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    • 在這篇論文中,我們討論二階非線性系統守恆律的整體經典解存在性.使用特徵線法和A uniform a priori estimate我們去建立整體經典解的存在條件.

    In this thesis, we consider the Cauchy problem of 2 × 2 nonlinear hyperbolic balance laws whose source terms consist of the integral of unknowns. Such nonlinear balance laws arise in, for instance, the compressible Euler-Poisson equations of gas dynamics in Lagrangian coordinate. We are concerned with the global existence of classical solutions to the Cauchy problem of such differential-integro systems. We extend the results by Ta-tsien Li for quasilinear hyperbolic systems to our nonlinear balance laws. The method in this thesis based on the following three steps: (1) the theory of local classical solutions, (2) uniform a priori estimate, (3) global existence or blow up of classical solutions. We find the transformation so that the 2 × 2 system for the first derivatives of Riemann invariants are de-coupled under this transformation. So, the characteristic method for scalar equations can be applied.

    中文摘要.................................................ⅰ 英文摘要.................................................ⅱ 1. Introduction...........................................2 2. Homogeneous System.....................................4 3. Non-homogeneous System................................10 4. Perturbed p-System with Source Term in Integral Form..13 5. A Uniform a-Priori Estimate...........................15 6. The Construction of h and Q...........................21 References...............................................23

    C. Dafermos, Generalized characteristics and the structure of solutions of hyperbolic conservation laws, Ind. Univ.Math. J., 26, pp.1097-1119, 1977.
    C. Dafermos, Solutions of the Riemann problem for a class of conservation laws by the viscosity method, Arch. Ration. Meeh. Anal., 52, pp. 1-9, 1973.
    C. Dafermos and L. Hsiao, Hyperbolic systems of balance laws with inhomogeneity and dissipation, Indiana U. Math. Journal, 31,No.4, pp. 471-491, 1982.
    G. Dal Maso, P. LeFloeh and F. Murat, Definition and weak stability of noneonservative products,J. Math. Pure. Appl., 74, pp. 483-548, 1995.
    Ronald J. DiPerna, Measure-Valued Solutions to Conservation Laws,Arch. Ration. Meeh. Anal., 88 , No.3, pp. 223-270. 31, 1985
    J. Glimm, Solutions in the large for nonlinear hyperbolic
    systems of equations, Comm. Pure Appl. Math., 18, pp.697-715, 1965.
    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. Equations, 222, pp. 515-549, 2006.
    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, pp.819-857, 2004.
    J. M. Hong and P. G. LeFloch,A version of Glimm method based on generalized Riemann problem, Portugaliae Mathematica 64, Fasc. 2, pp. 199-236, 20007.
    E. Isaacson and B. Temple, Convergence of 2 x 2 by Godunov
    method for a general resonant nonlinear balance law,SIAM J.
    Appl. Math.55, pp. 625-640, 1995.
    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. Rozanovaed., Nova Press, 2004.
    S. Kruzkov, First order quasilinear equations with several space variables,Math. USSR Sbornik, 10, pp. 217-243, 1970.
    P. D. Lax, Hyperbolic system of conservation laws, II, Comm. Pure Appl.Math., 10, pp. 537-566, 1957.
    P. G. LeFloch, Entropy weak solutions to nonlinear hyperbolic systems under nonconservative form,Comm. Partial Differential Equations,13, pp. 669-727, 1988.
    Ta-tsien Li, Global Classical solutions for quasilinear hyperbolic systems, Research in Applied Math.,Wiley Press.
    Fagui Liu, Cauchy problem for quasilinear hyperbolic systems,Yellow River Conservancy Press.
    T. P. Liu, The Riemann problem for general systems of conservation laws,J. Diff.Equations, 18, pp. 218-234, 1975.
    T. P. Liu, Quaslinear hyperbolic systems,Comm. Math.Phys., 68, pp. 141-172,1979.
    C. Mascia and C. Sinestrari, The perturbed Riemann problem for a balance law,Advances in Differential Equations, 2,pp. 779-810, 1997.
    O. A. Oleinik,Discontinuous solutions of nonlinear differential equations,Amer. Math. Soc. Transl. Ser. 2, 26, pp. 95-172. 32, 1957.
    C. Sinestrari, The Riemann problem for an inhomogeneous
    conservation law without convexity, SIAM J. Math. Anal., 28,No.1, pp. 109135, 1997.
    C. Sinestrari, Asymptotic profile of solutions of conservation laws with source, Diff. and Integral Equations, 9, No.3, pp. 499-525, 1996.
    J.Smoller, Shock waves and reaction-dffusion equations,Springer,New York, 1983.
    A. Tzavaras, Waves interactions and variation estimates for self-similar zero viscosity limits in systems of conservation laws, Arch. Ration. Mech. Anal., 135, pp. 1-60, 1996.
    A. Volpert, The space BV and quasilinear equations,Maths. USSR Sbornik 2, pp. 225-267,1967

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