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

Diehl, Stefan LU (2009) In Journal of Hyperbolic Differential Equations 6(1). p.127-159
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.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Degenerate parabolic equation, nonlinear scalar convection-diffusion equation, conservation law, discontinuous coefficient, uniqueness, coupling condition, interface entropy condition
in
Journal of Hyperbolic Differential Equations
volume
6
issue
1
pages
127 - 159
publisher
World Scientific
external identifiers
  • wos:000264556200004
  • scopus:65449143904
ISSN
1793-6993
DOI
10.1142/S0219891609001794
language
English
LU publication?
yes
id
934fbed9-9547-4b22-854b-06cf7988fcba (old id 1219478)
date added to LUP
2009-04-14 16:04:49
date last changed
2017-08-13 04:33:06
@article{934fbed9-9547-4b22-854b-06cf7988fcba,
  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.},
  author       = {Diehl, Stefan},
  issn         = {1793-6993},
  keyword      = {Degenerate parabolic equation,nonlinear scalar convection-diffusion equation,conservation law,discontinuous coefficient,uniqueness,coupling condition,interface entropy condition},
  language     = {eng},
  number       = {1},
  pages        = {127--159},
  publisher    = {World Scientific},
  series       = {Journal of Hyperbolic Differential Equations},
  title        = {A uniqueness condition for nonlinear convection-diffusion equations with discontinuous coefficients},
  url          = {http://dx.doi.org/10.1142/S0219891609001794},
  volume       = {6},
  year         = {2009},
}