#### Null controllability of a nonlocal heat equation with integral kernel

U. Biccari, V. Hernández-Santamaría Null controllability of a nonlocal heat equation with integral kernel, DOI: Abstract: We consider a linear nonlocal heat equation in a bounded domain $\Omega\subset\mathbb{R}^d$ with Dirichlet boundary conditions. The non-locality is given by the presence of an integral kernel. We analyze the problem of controllability when the control acts on a…

#### Null-controllability properties of a fractional wave equation with a memory term

U. Biccari, M. Warna Null-controllability properties of a fractional wave equation with a memory term Abstract: We study the null-controllability properties of a one-dimensional wave equation with memory associated with the fractional Laplace operator. The goal is not only to drive the displacement and the velocity to rest at some time-instant but also to require…

#### Null-controllability properties of the wave equation with a second order memory term

U. Biccari, S. Micu Null-controllability properties of the wave equation with a second order memory term,doi.org/10.1016/j.jde.2019.02.009 Abstract: We study the internal controllability of a wave equation with memory in the principal part, defined on the one-dimensional torus $\mathbb{T}=\mathbb{R}/2\pi\mathbb{Z}$. We assume that the control is acting on an open subset $\omega(t)\subset\mathbb{T}$, which is moving with a…

#### Dynamics and control for multi-agent networked systems: a finite difference approach

U. Biccari, D. Ko, E. Zuazua Dynamics and control for multi-agent networked systems: a finite difference approach Abstract: We analyze the dynamics of multi-agent collective behavior models and their control theoretical properties. We first derive a large population limit to parabolic diffusive equations. We also show that the non-local transport equations commonly derived as the…