A new approach to constrained systems with a convex extension


Systems S of N partial differential equations are considered, with M differential constraints and satisfying a convex supplementary conservation law. When M = 0, it is well known that these systems assume the symmetric hyperbolic form if the components of the mean field are taken as independent variables. To extend this property to the case M≠ 0, a new system S<sup>*</sup> is here proposed with M supplementary variables x<sub>A</sub> such that the solutions of S<sup>*</sup> with x<sub>A</sub> = 0 are those of the system S. Moreover S can be expressed in the symmetric hyperbolic form. This methodology is tested by applying it to the equations of the superfluid, modified from the classical Landau's formulation.

DOI Code: 10.1285/i15900932v16n2p173

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