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

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Author

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.

Department/s

Publishing year

2009

Language

English

Pages

127-159

Publication/Series

Journal of Hyperbolic Differential Equations

Volume

6

Issue

1

Document type

Journal article

Publisher

World Scientific Publishing

Topic

  • Mathematics

Keywords

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

Status

Published

Research group

  • Partial differential equations

ISBN/ISSN/Other

  • ISSN: 1793-6993