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Article Dans Une Revue Communications in Mathematical Sciences Année : 2016

The symmetric structure of the Green-Naghdi type equations

Résumé

The notion of symmetry classically defined for hyperbolic systems of conservation laws is extended to the case of evolution equations of conservative form for which the flux function can bean operator. We explain how such a symmetrization can work from a general point of view using an extension of the classical Godunov structure. We then apply it to the Green–Naghdi type equations which are a dispersive extension of the hyperbolic shallow-water equations. In fact, in the case of these equations, the general Godunov structure of the system is obtained from its Hamiltonian structure.
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Dates et versions

hal-01074488 , version 1 (16-10-2014)
hal-01074488 , version 2 (15-12-2014)
hal-01074488 , version 3 (09-04-2015)
hal-01074488 , version 4 (31-08-2016)

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Dena Kazerani. The symmetric structure of the Green-Naghdi type equations. Communications in Mathematical Sciences, 2016, 14 (7), pp.1925-1946. ⟨10.4310/CMS.2016.v14.n7.a7⟩. ⟨hal-01074488v4⟩
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