ON TWO PROBLEMS INVOLVING NONLOCAL HYPERBOLIC CONSERVATION LAWS

In this talk, I will consider two problems involving nonlocal hyperbolic con- servation laws. The rst problem (1) is about giving a sense to a hyperbolic conservation law with a constraint on the gradient of the solution. This is not straightforward since conservation laws naturally develop discontinuities in which the gradient explodes. I give a sense to this problem by considering a related conservation law with a nonlocal term, and prove existence, uniqueness and stability of solution of the Cauchy problem. In the second part, I will consider a class of nonlocal conservation laws used in recent years to study crowd dynamics. I will present a convergence result for numerical approxima- tions of this nonlocal model. The second part is a collaboration with Rinaldo Colombo (Brescia) and Andreia Teixeira (Lisboa). |||||||||||||||| ||