Existence, uniqueness and regularity results on nonlocal balance laws

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A general result on the approximation of local conservation laws by nonlocal conservation laws: The singular limit problem for exponential kernels (2020, background): “Our “nonlocal-to-local convergence” result closes the gap between local and nonlocal modelling of phenomena governed by conservation laws; moreover, it provides a way of defining the entropy admissible solutions of local conservation laws as limits of weak solutions to nonlocal conservation laws, wh”
Global entropy weak solutions for general non-local traffic flow models with anisotropic kernel (2018, methodology): “We observe that, for a close class of non-local equations, uniqueness of solutions has been recently derived in [13] relying on characteristics method and a ﬁxed-point argument, thus avoiding the use of entropy conditions.”