Abstract

PEREZ, Edgardo  and  ROZGA, Krzysztof. Hyperbolicity and genuine nonlinearity conditions for certain p-systems of conservation laws, week solutions and the entropy condition. Integración - UIS [online]. 2017, vol.35, n.1, pp.11-36. ISSN 0120-419X.  https://doi.org/10.18273/revint.v35n1-2017002.

We consider a p-system of conservation laws that emerges in one dimensional elasticity theory. Such system is determined by a function W. We consider four forms of W. These are St.Venant-Kirchhoff, Ogden, Kirchhoff modified, Blatz-Ko-Ogden forms. In each of those cases we determine the conditions for the parameters µ, λ and f, under which the corresponding system is hyperbolic and genuinely nonlinear. We also establish what it means a weak solution of an initial and boundary value problem. Finally we ask if such solutions satisfy the entropy condition. For a standard entropy function we provide a complete answer, except of the Blatz-Ko-Ogden case. For a general strictly convex entropy function the result is that for the initial value of velocity fun

Keywords : Weak solution; entropy condition; conservation laws; genuinely nonlinear; p-system..

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