Coupling techniques for nonlinear hyperbolic equations. II. Resonant interfaces with internal structure - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Networks and Heterogeneous Media Année : 2021

Coupling techniques for nonlinear hyperbolic equations. II. Resonant interfaces with internal structure

Résumé

In the first part of this series, an augmented PDE system was introduced in order to couple two nonlinear hyperbolic equations together. This formulation allowed the authors, based on Dafermos's self-similar viscosity method, to establish the existence of self-similar solutions to the coupled Riemann problem. We continue here this analysis in the restricted case of one-dimensional scalar equations and investigate the internal structure of the interface in order to derive a selection criterion associated with the underlying regularization mechanism and, in turn, to characterize the nonconservative interface layer. In addition, we identify a new criterion that selects double-waved solutions that are also continuous at the interface. We conclude by providing some evidence that such solutions can be non-unique when dealing with non-convex flux-functions.
Fichier principal
Vignette du fichier
2010.01565.pdf (1.17 Mo) Télécharger le fichier
Origine : Publication financée par une institution

Dates et versions

hal-02962629 , version 1 (09-01-2024)

Identifiants

Citer

Benjamin Boutin, Frédéric Coquel, Philippe G. Lefloch. Coupling techniques for nonlinear hyperbolic equations. II. Resonant interfaces with internal structure. Networks and Heterogeneous Media, 2021, 16 (2), pp.283-315. ⟨10.3934/nhm.2021007⟩. ⟨hal-02962629⟩
75 Consultations
9 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More