ANZIAM J. 49 (2007), no. 1, pp. 39–52.

Evolution equations having conservation laws with flux characteristics

B. van Brunt M. Vlieg-Hulstman
Institute of Fundamental Sciences
Mathematics Department
Massey University
New Zealand
B.vanBrunt@massey.ac.nz
Institute of Fundamental Sciences
Mathematics Department
Massey University
New Zealand
Received 9 August 2006

Abstract

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.

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2000 Mathematics Subject Classification: primary 35K
(Metadata: XML, RSS, BibTeX) MathSciNet: MR2378148 Z'blatt-MATH: pre05243890
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