Uniqueness of the Entropy Solutions to Cauchy Problem for a Degenerate Parabolic-Hyperbolic Equation

Journal of Shanghai Jiaotong University ›› 2011, Vol. 45 ›› Issue (07): 1085-1090.

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Uniqueness of the Entropy Solutions to Cauchy Problem for a Degenerate Parabolic-Hyperbolic Equation

HAO Xing-Wen-1, 2 , WANG Qin-1

(1. Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, China; 2. School of Mathematics and Information Sciences, Weifang University, Weifang 261061, Shandong, China)

Received:2010-06-10 Online:2011-07-29 Published:2011-07-29

Abstract

Abstract: Kuznetsov’s method is a useful tool to establish the error estimate between numerical solutions and entropy weak solution for hyperbolic equation. This paper uses this method to prove the uniqueness to the Cauchy problem of a special example of second order degenerate parabolic-hyperbolic equation, Meanwhile, the paper obtained that entropy solutions are continuous at t=0 in the sense of L1 norm by the double variable device.

Key words: Kuznetsov method, degenerate parabolichyperbolic equation, entropy solutions,, error estimate

CLC Number:

O175.27

HAO Xing-Wen-1, 2 , WANG Qin-1. Uniqueness of the Entropy Solutions to Cauchy Problem for a Degenerate Parabolic-Hyperbolic Equation[J]. Journal of Shanghai Jiaotong University, 2011, 45(07): 1085-1090.

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Uniqueness of the Entropy Solutions to Cauchy Problem for a Degenerate Parabolic-Hyperbolic Equation

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