Abstract
In view of the modeling of uncertainties which propagate in non linear transport equations and general hyperbolic systems, we review some recent alternatives to the classical moment method. These approaches are obtained by reconsidering the non linear structure with entropy considerations. It is shown that the entropy variable and the kinetic formulation of conservation laws yield new approaches with strong control of the maximum principle. A general minimization principle is proposed for these kinetic polynomials, together with an original reformulation as an optimal control problem. Basic numerical illustrations show the properties of these new techniques. A surprising linked to quaternion algebras is evoked in relation with kinetic polynomials. Natural limitations are discussed in the conclusion.
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