On the well-posedness for the coupling of multidimensional quasilinear diffusion-transport equations

• Autores: Gloria Aguilar Villa, Laurent Lévi
• Localización: Monografías de la Real Academia de Ciencias Exactas, Físicas, Químicas y Naturales de Zaragoza, ISSN 1132-6360, Nº. 38, 2012 (Ejemplar dedicado a: Monique Madaune-Tort), págs. 65-84
• Idioma: inglés
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• Resumen

  • This paper deals with the coupling of a quasilinear parabolic problem with a first order hyperbolic one in a multidimensional bounded domain n . In a region p a diffusion-advection-reaction type equation is set while in the complementary h ≡ \ p, only advection-reaction terms are taken into account. Suitable transmission conditions along the interface ∂ p ∩ ∂ h are required. We select a weak solution characterized by an entropy inequality on the whole domain. This solution is given by a vanishing viscosity method.