A uniqueness condition for nonlinear convection-diffusion equations with discontinuous coefficients

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Abstract

The paper focuses on the uniqueness issue for scalar convection-diffusion equations where both the convective flux and diffusion functions have a spatial discontinuity. An interface entropy condition is proposed at such a spatial discontinuity. It implies the Kružkov-type entropy condition presented by Karlsen et al. in 2003. They proved uniqueness when the convective flux function satisfies an additional "crossing condition". The crossing condition becomes redundant with the entropy condition proposed here. Thereby, more general flux functions are allowed. Another advantage of the entropy condition is its simple geometrical interpretation, which facilitates the construction of stationary solutions.

Detaljer

Författare
Enheter & grupper
Forskningsområden

Ämnesklassifikation (UKÄ) – OBLIGATORISK

  • Matematik

Nyckelord

Originalspråkengelska
Sidor (från-till)127-159
TidskriftJournal of Hyperbolic Differential Equations
Volym6
Utgåva nummer1
StatusPublished - 2009
PublikationskategoriForskning
Peer review utfördJa