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Properties of Characteristics to the Conservation Laws Equation

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Author: Zhenmin Zhao, Yinchuan Zhao

Abstract: This paper is mainly concerned with the properties of the characteristics to the Conservation Laws Equation. Considering the relationship between a potential function`s minimum points and the points on the characteristics. Then the characteristics are divided into two parts. At the same time we also give the classification standard of the characteristics. Finally, based on the research of the literature [3], do not require the initial condition tends to zero at infinity, we also can get the same conclusion, And it applies a wider range.

Keywords: Conservation Law; characteristics; Non-degenerate minimum point;

References:

[1] Lax, P. D, Hyperbolic systems of conservation laws Ⅱ, Comm. Pure. Appl. Math, 10(1957)

[2] Schaeffer .D. G, A regularity theorem for conservation law [J]. Advances in Mathematics, 1973, Vol. 11: 368-386

[3] 李邦河, 王靖华. 单个守恒律解的大范围定性研究[J]. 北京: 中国科学, 1979, (S1): 12-2

[4] Yinchuan Zhao, Tao Tang, Jing hua Wang, Regularity and Global Structure of Solution to Hamilton-Jacobi Equations I. Convex Hamiltonians[J], Journal of Hyperbolic Differential Equations, Vol. 5, No. 3(2008): 663-680

[5] Wang J., Regularity of entry solutions to no convex scalar conservation laws with monotone initial data, Acted Mathematica Scientia, 2009, Vol.29(No. 3): 613-628

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