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Error Bounds for Glimm Difference Approximations for Scalar Conservation Laws Without Convexity

Error Bounds for Glimm Difference Approximations for Scalar Conservation Laws Without Convexity
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摘要 In last century, D. Hoff and J. Smoller derived the error bounds for the Glimm difference approximations of the solutions to scalar conservation laws with convexity. Our work is to extend the corresponding result of them to the case without convexity. In last century, D. Hoff and J. Smoller derived the error bounds for the Glimm difference approximations of the solutions to scalar conservation laws with convexity. Our work is to extend the corresponding result of them to the case without convexity.
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2006年第4期1271-1282,共12页 数学学报(英文版)
基金 the foundations of the National Natural Science Committee(10171112) the Natural Science Committee of Guangdong Province(05003348)
关键词 error bounds Glimm's scheme non-convexity error bounds, Glimm's scheme, non-convexity
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参考文献7

  • 1Glimm, J.: Solutions in the large for nonlinear hyperbolic systems of equatons. Comm. Pure Appl. Math.,18, 697-715 (1965)
  • 2Hoff, D., Smoller, J.: Error bounds for Glimm difference approximations for scalar conservation laws. Trans.Amer. Math. Soc., 289, 611-642 (1985)
  • 3Krushkov, S. N.: First-srder quasilinear equation in sevral space variables. Math. USSR Sb., 10, 217-273(1970)
  • 4Liu, T. P.: The deterministic version of the Glimm scheme. Comm. Math. Phys., 57, 135-148 (1977)
  • 5Oleinik, 0.: Uniqueness and stability of the generalized solution of the Cauchy problem for a quasilinear equation. Usp. Mat. Nauk, 14, 165-170 (1959), Amer. Math. Soc. Transl. Ser. 2, 33, 285-290 (1964)
  • 6Smoller, J.: Shock waves and reaction-diffusion equations, Springer-Verlag, New York, 1995
  • 7Liu, T. P.: Asmissible solutions of hyperbolic conservation laws. Memoirs of Amer. Meth. Soc., 30, 240(1981)

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