Wave features of a hodograph-like transformation for quasilinear hyperbolic systems

We study the properties of a variables transformation for a 2×2 quasilinear hyperbolic nonhomogeneous system of first order, related to wave propagation. The considered variables transformation transforms characteristic curves of the original system, into characteristic curves of the transformed system. We make use of this property to study the propagation of weak discontinuities (acceleration waves) compatible with the quasilinear system (1.1). Finally a special class of rate-type media is considered and asymptotic solutions are investigated.

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Sommario Si studiano le proprietà di una trasformazione di variabili per un sistema quasilineare iperbolico del primo ordine non omogeneo. La trasformazione considerata trasforma curve caratteristiche del sistema originale in curve caratteristiche del sistema trasformato. Utilizzando queste proprietà si studia la propagazione delle onde di discontinuità (onde di accelerazione) compatibile con il sistema quasilineare iperbolico considerato e si cercano soluzioni asintotiche.

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This work was supported by the C.N.R. through the G.N.F.M. and partially under contract No. 88. 01855.01.