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On a representation of the prolonged systems for a scalar conservation law and on higher-order entropies

  • Partial Differential Equations
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Abstract

We find a representation of prolonged systems in the form of an equation on a commutative matrix algebra. This representation is used to obtain a complete description of the entropies of the prolonged systems. In particular, we show that, for an essentially nonlinear equation, all such entropies are obtained by formal differentiation of “scalar” entropies.

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References

  1. Lax, P.D., Shock Waves and Entropy, in Contributions to Nonlinear Functional Analysis (Proc. Sympos., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1971), New York: Academic, 1971, pp. 603–634.

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Authors and Affiliations

  1. Novgorod State University, Novgorod, Russia

    E. Yu. Panov

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  1. E. Yu. Panov
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Original Russian Text © E.Yu. Panov, 2008, published in Differentsial’nye Uravneniya, 2008, Vol. 44, No. 12, pp. 1694–1699.

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Panov, E.Y. On a representation of the prolonged systems for a scalar conservation law and on higher-order entropies. Diff Equat 44, 1758–1763 (2008). https://doi.org/10.1134/S0012266108120124

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  • DOI: https://doi.org/10.1134/S0012266108120124

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