On the local limit of nonlocal conservation laws

Periodic seminar of the Department of Mathematics
5 December 2023
Start time 
2:30 pm
PovoZero - Via Sommarive 14, Povo (Trento)
Seminar Room "1"
Target audience: 
University community
UniTrento students
Contact person: 
Andrea Pinamonti, Andrea Marchese, Paolo Bonicatto
Contact details: 
Università degli Studi Trento 38123 Povo (TN) - Staff Dipartimento di Matematica
+39 04 61/281508-1625-1701-3786-1980
Laura Spinolo (CNR IMATI Pavia)


Consider a so-called nonlocal conservation law, that is a continuity equation where the velocity field depends on the solution through the convolution with a given kernel. In the singular limit where the convolution kernel is replaced by a Dirac delta, one formally recovers a scalar conservation law. In this talk I will address the following question: can we rigorously justify this formal limit? In general, this is not possible, as shown by explicit counterexamples.
However, in the specific framework of traffic models (with anisotropic convolution kernels) convergence results have been recently established, under suitable assumptions. My presentation will be based on joint works with Maria Colombo, Gianluca Crippa and Elio Marconi.

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