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math.AP2022★ 5 cited
Conservation laws with nonlocal velocity -- the singular limit problem
Jan Friedrich, Simone Göttlich, Alexander Keimer +1
We consider conservation laws with nonlocal velocity and show for nonlocal weights of exponential type that the unique solutions converge in a weak or strong sense (dependent on th…
math.AP2021★ 2 cited
Discontinuous nonlocal conservation laws and related discontinuous ODEs -- Existence, Uniqueness, Stability and Regularity
Alexander Keimer, Lukas Pflug
We study nonlocal conservation laws with a discontinuous flux function of regularity in the spatial variable and show existence and uniqueness of…
math.AP2020★ 2 cited
A general result on the approximation of local conservation laws by nonlocal conservation laws: The singular limit problem for exponential kernels
Giuseppe Maria Coclite, Jean-Michel Coron, Nicola De Nitti +2
We deal with the problem of approximating a scalar conservation law by a conservation law with nonlocal flux. As convolution kernel in the nonlocal flux, we consider an exponential…