We study the surface diffusion flow in the flat torus, that is, smooth hypersurfaces moving with the outer normal velocity given by the Laplacian of their mean curvature. This model describes the evol...
We introduce a general framework for the study of numerical approximations of a certain class of solutions, called stable solutions, of second order mean-field game systems for which uniqueness of sol...
We discuss a novel class of swarm-based gradient descent (SBGD) methods for non-convex optimization. The swarm consists of agents, each is identified with position, x, and mass, m. There are three key...
In this talk I will discuss some results about long time behaviors of solutions to Hamiltonian PDEs (Schrödinger, Kirchhoff, etc). In particular I will focus on a recent result where we (with J. Berni...
We are interested here in questions related to the maximal regularity of solutions of elliptic problems with Dirichlet boundary condition (see [1]). For the last 40 years, many works have been concern...
We study a system of nonlocal aggregation cross-diffusion PDEs that describe the evolution of opinion densities on a network. The PDEs are coupled with a system of ODEs that describe the time evolutio...
We discuss regularity for the crack set of a minimizer for the Griffith fracture energy, arising in the variational modeling of brittle materials. In the planar setting, we prove an epsilon-regulari...
The research project, in collaboration with Thales Alenia Space Italia SpA, aims to study, develop and numerically simulate innovative methods for optimizing the orbital transfer of small satellites i...
Over the last few decades, the study of the nonlinear Schrödinger equation on \(\mathbb{R}^N\) has been investigated by numerous researchers. However, very few results are known when the domain is non...
In a recent paper, we study the long--time behavior and the stability of the surface diffusion flow of smooth hypersurfaces in the flat torus \(\mathbb T^n\). According to this flow, smooth hypersurfa...
In this talk we consider inverse problems for the partial differential equations describing the behavior of certain fluids. Our focus will be on the fluid-structure interaction problem and the object...
Effective feedback control is essential for optimizing dynamical systems by minimizing a predefined cost function, thereby stabilizing the system toward a desired state. Despite its proven effectivene...
