Abstracts

Nonlocal Conservation Laws with Memory and Their Zero Retention Limit

Ganesh Vaidhya,  IISc Bangalore

We discuss entropy solutions for a class of nonlocal conservation laws in which the convective flux is convolved with a kernel in both space and time. This formulation captures spatial interactions as well as dependence on past states, thereby incorporating memory effects. We analyze the asymptotic behavior as the support of the temporal kernel shrinks and establish a memory-to-memoryless limit: entropy solutions converge to those of the corresponding model that is nonlocal only in space. We further derive convergence rate estimates for this limit. Finally, we prove that the proposed numerical schemes are asymptotically compatible with the memoryless limit by deriving corresponding convergence rates.