Entropy solutions of nonlocal scalar conservation laws with congestion
A talk in the Oberseminar Analysis series by
Emanuela Radici from U L’Aquila
| Abstract: | In this talk we consider a class of scalar nonlinear models describing
crowd dynamics. The congestion term appears in the transport equation
in the form of a compactly supported nonlinear mobility function, thus
making standard weak-type compactness arguments and uniqueness of
weak solutions fail. We introduce two different approaches to the problem
and discuss their connections with the wellposedness of entropy solutions
of the target pde in the sense of Kruˇzkov. A deterministic particle ap-
proach relying on suitable generalisations of the Follow-the-leader scheme,
which can be interpreted as the Lagrangian discretisations of the problem;
and a variational approach in the spirit of a minimising movement scheme
exploiting the gradient flow structure of the evolution in a suitable metric
framework. Zoom Meeting ID: 686 0112 3008 Passcode: 867330 $\href{https://uni-bielefeld.zoom-x.de/j/68601123008?pwd=3B0C4nRNJveeJ71WQ1caCai3MbXTwA.1}{\textbf{Join Zoom Meeting}}$ Within the CRC this talk is associated to the project(s): A8 |