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

In English

Författare

Summary, in English

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.

Avdelning/ar

Publiceringsår

2009

Språk

Engelska

Sidor

127-159

Publikation/Tidskrift/Serie

Journal of Hyperbolic Differential Equations

Volym

6

Issue

1

Dokumenttyp

Artikel i tidskrift

Förlag

World Scientific Publishing

Ämne

  • Mathematics

Nyckelord

  • Degenerate parabolic equation
  • nonlinear scalar convection-diffusion equation
  • conservation law
  • discontinuous coefficient
  • uniqueness
  • coupling condition
  • interface entropy condition

Status

Published

Forskningsgrupp

  • Partial differential equations

ISBN/ISSN/Övrigt

  • ISSN: 1793-6993