**Césare Molinari** was PhD student in Applied Mathematics at Universidad Técnica Federico Santa María (Valparaíso, Chile). His scientific interests were related to numerical algorithms for maximal monotone variational inequalities and convex non-differentiable optimization. In this context, his research was focused on the design of the algorithms, on the analysis of the asymptotic properties and of the rate of convergence. This theory finds natural applications in sparse optimal control of PDEs and reconstruction of images. He was doing an internship in Control Theory under the joint supervision of professor Enrique Zuazua.

#### Author's contribution:

#### Turnpike property for functionals involving $L^1$−norm

We want to study the following optimal control problem...