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1 results

  • Evolution equations having conservation laws with flux characteristics

  • B. Van Brunt, M. Vlieg Hulstman
  • Journal:
    The ANZIAM Journal / Volume 49 / Issue 1 / July 2007
    Published online by Cambridge University Press:
    17 February 2009, pp. 39-52
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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.