Evolution equations having conservation laws with flux characteristics

• Autores: Bruce van Brunt, M. Vlieg-Hulstman
• Localización: Anziam journal: The Australian & New Zealand industrial and applied mahtematics journal, ISSN 1446-1811, Vol. 49, Nº 1, 2007, págs. 39-52
• Idioma: inglés
• DOI: 10.1017/s1446181100012669
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• Resumen

  • A class of evolution equations in divergence form is studied in this paper. Specifically, we develop conditions under which the spatial divergence term, the flux, corresponds to the characteristic of a conservation law. The KdV equation is a prominent example of an equation having a flux term that is also a characteristic for a conservation law. We show that the flux term must be self-adjoint. General equations for the corresponding conservation laws and Hamiltonian densities are derived and supplemented with examples.