A simple yet extremely valuable approach to the study of the climate system comes from the use of Energy Balance Models (EBMs), which had originally been introduced in the sixties independently by Budyko and Sellers. Such models
describe in a simplified yet effective way the evolution of the zonally averaged
temperature on the Earth's surface, thus reducing the problem to a single 1D...
In this talk we introduce the Energy Balance Climate Models (EBCM), then we discuss some results concerning the approximate multiplicative controllability of reaction-diffusion equations, also degenerate with the application to a particular EBCM, that is the Budyko-Sellers model. We also present some interesting open problems and new research directions.
In this talk I will give an overview on response theory for stochastic PDEs, with a particular interest on its potential for energy balance models. With response theory we mean in this context the following: studying the regularity of averages of observables against the stationary distribution with respect to changes in relevant system parameters, in particular their differentiability (linear...
The term data assimilation from the geosciences refers to reconstructing the current state of a dynamical system from current and past observations of the system. Here "current'' and "past'' refer to the time in which the system evolves.
By "observation'' we mean the value of a function taken at the current state of the system; these observation functions are typically not injective. The...
The QG equations incorporate the most important balances in rotating geophysical fluid dynamics, the hydrostatic and the geostrophic balance. Furthermore, they reflect some thermodynamical aspects of the fluid as well. These equations form the simplest models that contain most important dynamical phenomena of ocean and atmosphere dynamics at mid-latitude. After the systematical derivation by...
We study a mathematical model to describe the evolution of a city, which is determined by the interaction of two large populations of agents, workers and firms. The map of the city is represented by a network with the edges representing at the same time residential areas and communication routes. We obtain a two population Mean-Field Game system coupled with an Optimal Transport problem...
One of the main features of the global climate is that it incorporates a very wide range of length and time scales and associated physical processes. Therefore it is important to understand which phenomena occur according to the use of single scales or to the interactions of them (i.e. internal gravity waves, Rossby waves, cloud formation). From a mathematical point of view, these various...
We study the controllability of the continuity equation where the dynamics follows a control-affine system without drift. Under suitable regularity conditions, the controllability of the system is a sufficient condition for achieving controllability of the continuity equation. Moreover, we show the existence of controls such that the flow of the control system is the optimal transport map, for...
We study the joint determination of optimal investment and optimal depollution in a spatiotemporal framework where pollution is transboundary and spatial component is described by a network structure. Pollution is controlled at a global level by a central planner. The problem is solved explicitly and the optimal investment and depollution are found. In conclusione, some investigations on the...
We analyze a Hegselmann-Krause type opinion formation model for a system of two populations. The two groups interact with each other via subsets of individuals, namely the leaders, and natural time delay effects are considered. By using careful estimates on the system’s trajectories, we prove that all agents asymptotically converge to a consensus state. Some future research directions as well...
A one-dimensional energy balance model (1D-EBM) is a simplified climate model that describes the evolution of Earth's temperature based on the planet's energy budget.
In this study, we examine a 1D-EBM that incorporates a parameter representing the impact of carbon dioxide on the energy balance. Based on empirical studies showing that bistability may occur in Earth's tropics, we consider...
