Solutions for a Nonlocal Conservation Law with Fading Memory
Abstract
Global entropy solutions in
BV
for a scalar nonlocal conservation law with fading memory are constructed as limits of vanishing viscosity approximate solutions. The uniqueness and stability of entropy solutions in
BV
are established, which also yield the existence of entropy solutions in
L
∞
while the initial data is only in
L
∞
. Moreover, if the memory kernel depends on a relaxation parameter $\de>0$ and tends to a delta measure weakly as measures when $\de\to 0+$, then the global entropy solution sequence in
BV
converges to an admissible solution in
BV
for the corresponding local conservation law.