On approximation of local conservation laws by nonlocal conservation laws
By Alexander Keimer, Lukas Pflug. Journal of Mathematical Analysis and Applications, 2019
67 citations recorded by the source corpus.
Abstract We show that for monotone initial datum the solution of nonlocal conservation laws converges to the entropy solution of the corresponding local conservation laws when the nonlocal reach tends to zero. This particularly covers the principle cases of conservation laws: shocks and rarefactions. The considered problem is addressed by studying the Entropy of the nonlocal conservation laws in the limit and by exploiting the semi-explicit solution formula developed in [30] .
Subfields: Applied Mathematics, Astronomy and Astrophysics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/bbc60665262b4f5598a8bf05cc3fa15343498062
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In Applied Mathematics
- Alexander Keimer
- Lukas Pflug
- Jean-Michel Coron
- Giuseppe Maria Coclite
- Zhaoyang Yin
- Felisia Angela Chiarello
- Paola Goatin
In Mathematical Physics
- Alexander Keimer
- Lukas Pflug
- Jean-Michel Coron
- Giuseppe Maria Coclite
- Eduardo Cerpa
- Olivier Glass
- Emmanuelle Crépeau
- Zhaoyang Yin
Citations in the corpus
- A general result on the approximation of local conservation laws by nonlocal conservation laws: The singular limit problem for exponential kernels (2020, background): “Some numerical results concerning the convergence can already be found in [42].”