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Solutions for a Nonlocal Conservation Law with Fading Memory

Gui-Qiang Chen·Cleopatra Christoforou
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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 $L^\infty$ while the initial data is only in $L^\infty$. 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.

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Gui-Qiang Chen, Cleopatra Christoforou. 2006-10-16. Solutions for a Nonlocal Conservation Law with Fading Memory. https://arxiv.org/abs/math/0610469

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