| 非齐次守恒律方程分片光滑解的粘性方法 |
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| 引用本文： | 杨宏伟. 非齐次守恒律方程分片光滑解的粘性方法[J]. 高等学校计算数学学报, 2001, 23(3): 273-280 |
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| 作者姓名： | 杨宏伟 |
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| 作者单位： | 北京大学数学科学学院科学与工程计算系, |
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| 基金项目： | 中科院知识创新重要方向项目 (编号为 :KZCX2 2 0 8),973国家重点基础发展规划项目 (编号为 :G1 9990 3 2 80 1 )的资助 |
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| 摘 要： | 1 引 言考虑非齐次守恒律方程ut+f(u) x =g(u) , -∞ 0 ,(1 .1 )u(x,0 ) =u0 (x) , -∞ 0 , (1 .5)g∈ C3且 g是 Lipschitz连续的 ,Lipschitz系数为 L . (1 .6 )对于一般守恒律齐次方程 ,粘性解逼近熵解的收敛阶为 O(ε ) [1 ] .在 f严格凸的条件下 ,其收敛速度可以提高到 O(ε|lnε|+ε) [2 ] ,[3] .本文考虑具有条件 (1 .5) (1 .6 )的非齐次方程(1 .1 ) ,在较广泛的一类初值条件下…
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| 关 键 词： | 非齐次守恒律方程 粘性方程 分片光滑解 粘性解 收敛阶 |
| 修稿时间： | 1999-11-11 |
VISCOSITY METHODS FOR PIECEWISE SMOOTH SOLUTIONS TO NONHOMOGENEOUS SCALAR CONSERVATIONS LAWS |
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| Yang Hongwei. VISCOSITY METHODS FOR PIECEWISE SMOOTH SOLUTIONS TO NONHOMOGENEOUS SCALAR CONSERVATIONS LAWS[J]. Numerical Mathematics A Journal of Chinese Universities, 2001, 23(3): 273-280 |
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| Authors: | Yang Hongwei |
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| Abstract: | It is proved that for nonhomogeneous scalar conservation laws, if the flux function is strictly convex, and the entropy solution is piecewise smooth with finitely many discontiuities (which includes initial central rarefaction waves, initial shocks, possible spontaneous formation of shocks in a future time and in teractions of all these patterns), then the error of viscosity solution to the inviscid solution is bounded by O(ε| lnε| ) in L1-norm. If neither central rarefaction waves nor spontaneous shocks occur, the error bound is improved to O(ε). |
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| Keywords: | nonhomogeneous scalar conservation laws error estimate viscosity methods piece-wise smooth. |
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