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Evolution equations having conservation laws with flux characteristics

Published online by Cambridge University Press:  17 February 2009

B. Van Brunt  and
M. Vlieg Hulstman
B. Van Brunt
Affiliation:
institute of Fundamental Sciences Mathematics Massey UniversityNew ZealandB.vanBrunt@massey.ac.nz
M. Vlieg Hulstman
Affiliation:
institute of Fundamental Sciences Mathematics Massey UniversityNew ZealandB.vanBrunt@massey.ac.nz
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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. 2000 Mathematics subject classification: primary 35K.

Keywords

evolution equationsconservation lawsHamiltonian densities
Type
Research Article
Information
The ANZIAM Journal , Volume 49 , Issue 1 , July 2007 , pp. 39 - 52
Copyright
Copyright © Australian Mathematical Society 2007

References

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