• K.T. JOSEPH
• P.G. LeFloch

Code(s) de Classification MSC:

Code(s) de Classification CR:

Résumé:

Abstract: Following pioneering work by Fan and Slemrod who studied the effect of artificial viscosity terms, we consider the system of conservation laws arising in liquid-vapor phase dynamics with physical viscosity and capillarity effects taken into account. Following Dafermos we consider self-similar solutions to the Riemann problem and establish uniform total variation bounds, allowing us to deduce new existence results. Our analysis covers both the hyperbolic and the hyperbolic-elliptic regimes and apply to arbitrarily large Riemann data.The proofs rely on a new technique of reduction to two coupled scalar equations associated with the two wave fans of the system. Strong L¹ convergence to a weak solution of bounded variation is established in the hyperbolic regime, while in the hyperbolic elliptic regime a stationary singularity near the axis separating the two wave fans, or more generally an almost-stationary oscillating wave pattern (of thickness depending upon the capillarity-viscosity ratio) are observed which prevent the solution to have globally bounded variation.

Mots Clés: ;

Date: 2006-12-18