Entropy solutions of scalar conservation laws are recovered as weak-star limits of nonlocal approximations with averaged fluxes via Hamilton-Jacobi stability.
Well-posedness of a conservation law with non-local flux arising in traffic flow modeling
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Existence and uniqueness of weak entropy solutions for nonlocal nonlinear scalar conservation laws is proven on short time horizons via fixed-point methods, extending to any finite horizon under additional assumptions.
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Nonlocal Approximation Principle for Entropy Solutions of Scalar Conservation Laws
Entropy solutions of scalar conservation laws are recovered as weak-star limits of nonlocal approximations with averaged fluxes via Hamilton-Jacobi stability.
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Existence and uniqueness of nonlocal nonlinear conservation laws via fixed-point methods
Existence and uniqueness of weak entropy solutions for nonlocal nonlinear scalar conservation laws is proven on short time horizons via fixed-point methods, extending to any finite horizon under additional assumptions.