A note on nonlocal approximations of sign-unrestricted solutions of conservation laws
- Resource Type
- Working Paper
- Authors
- Keimer, Alexander; Pflug, Lukas
- Source
- Subject
- Mathematics - Analysis of PDEs
35L65, 35L04
- Language
We study the singular limit problem for nonlocal conservation laws in which the sign of the initial datum is unrestricted and the velocity of the conservation law depends on a nonlocal approximation of the absolute value of the density. We demonstrate that the nonlocal solutions converge to the local entropy solution when the nonlocal kernel tends to a Dirac distribution, and thus obtain an approximation result for local unsigned conservation laws, generalizing the current results on the so-called sign-restricted singular limit problem. The considered model class covers special cases like a generalized Burgers' equation and scalar versions of the Keyfitz--Kranzer system.
Comment: 13 pages, 1 figure