| Autor: |
Coclite, Giuseppe Maria, Colombo, Maria, Crippa, Gianluca, De Nitti, Nicola, Keimer, Alexander, Marconi, Elio, Pflug, Lukas, Spinolo, Laura V. |
| Rok vydání: |
2023 |
| Předmět: |
|
| Druh dokumentu: |
Working Paper |
| Popis: |
We consider a class of nonlocal conservation laws with exponential kernel and prove that quantities involving the nonlocal term $W:=\mathbb{1}_{(-\infty,0]}(\cdot)\exp(\cdot) \ast \rho$ satisfy an Ole\u{\i}nik-type entropy condition. More precisely, under different sets of assumptions on the velocity function $V$, we prove that $W$ satisfies a one-sided Lipschitz condition and that $V'(W) W \partial_x W$ satisfies a one-sided bound, respectively. As a byproduct, we deduce that, as the exponential kernel is rescaled to converge to a Dirac delta distribution, the weak solution of the nonlocal problem converges to the unique entropy-admissible solution of the corresponding local conservation law, under the only assumption that the initial datum is essentially bounded and not necessarily of bounded variation. |
| Databáze: |
arXiv |
| Externí odkaz: |
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