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Rectifiability of entropy productions for weak solutions of the 2D eikonal equation with supercritical regularity
Xavier Lamy, Elio Marconi
Weak solutions of the eikonal equation \begin{align*} |m|=1\text{ a.e. and }\mathrm{div}\: m =0\,, \end{align*} arise naturally as shar…
On the regularity of continuous solutions to multidimensional scalar conservation laws with bounded source
Fabio Ancona, Laura Caravenna, Alexander J. Cliffe +1
We prove the Hölder regularity of continuous isentropic solutions to multi-dimensional scalar balance laws when the source term is bounded and the flux satisfies general assumption…
Well-posedness results for the Generalized Aw-Rascle-Zhang model
Elio Marconi, Laura V. Spinolo
We establish existence, uniqueness and stability results for the so-called Generalized Aw-Rascle-Zhang model, a second order traffic model introduced by Fan, Herty and Seibold. Our…
Nonlocal Generalized Aw-Rascle-Zhang model: well-posedness and singular limit
Elio Marconi, Laura V. Spinolo
We discuss a nonlocal version of the Generalized Aw-Rascle-Zhang model, a second-order vehicular traffic model where the empty road velocity is a Lagrangian marker governed by a tr…
Intermediate Domains for Scalar Conservation Laws
Fabio Ancona, Alberto Bressan, Elio Marconi +1
For a scalar conservation law with strictly convex flux, by Oleinik's estimates the total variation of a solution with initial data decay…
Ole\uınik-type estimates for nonlocal conservation laws and applications to the nonlocal-to-local limit
Giuseppe Maria Coclite, Maria Colombo, Gianluca Crippa +5
We consider a class of nonlocal conservation laws with exponential kernel and prove that quantities involving the nonlocal term $W:=\mathbb{1}_{(-\infty,0]}(\cdot)\exp(\cdot) \ast…