A uniqueness condition for nonlinear convection-diffusion equations with discontinuous coefficients
(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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1219478
- author
- Diehl, Stefan LU
- organization
- publishing date
- 2009
- 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 Publishing
- 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
- 2016-04-04 07:10:45
- date last changed
- 2022-01-29 01:49:38
@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}}, keywords = {{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 Publishing}}, 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}}, doi = {{10.1142/S0219891609001794}}, volume = {{6}}, year = {{2009}}, }