arXiv subjects

Giovanni Mascali

Publications and source records attributed to Giovanni Mascali.

5 recordsLinked to original sources

arXiv2026

Analysis and Optimal Design of Equilibria in the Vlasov-Poisson System

The optimal design of equilibrium particle distributions generated by external electric fields is investigated in the framework of stationary Maxwellian equilibria of the Vlasov-Poisson system. The resulting normalized Poisson-Boltzmann equation is analyzed, and existence and uniqueness of the self-consistent equilibrium potential are established by two complementary approaches. A Schauder fixed-point argument based on uniform estimates for the normalized nonlinear source and a variational approach based on a strictly convex free-energy functional are developed. Building upon these analytical results, a unified optimal design framework is formulated for equilibrium densities. Valley-potential, quadratic tracking, and Kullback-Leibler design criteria are treated within the same optimization framework. First-order optimality conditions are derived, and a projected nonlinear conjugate-gradient algorithm is proposed for the numerical solution of the resulting optimization problems.

math.OC↗

arXiv2024

An existence result in annular regions times conical shells and its application to nonlinear Poisson systems

We provide a new existence result for abstract nonlinear operator systems in normed spaces, by means of topological methods. The solution is located within the product of annular regions and conical shells. The theoretical result possesses a wide range of applicability, which, for concreteness, we illustrate in the context of systems of nonlinear Poisson equations subject to homogeneous Dirichlet boundary conditions. For the latter problem we obtain existence and localization of solutions having all components nontrivial. This is also illustrated with an explicit example in which we also furnish a numerically approximated solution, consistent with the theoretical results. We conclude with an application of our results to a reaction--diffusion Lotka--Volterra system with source terms for competing species.

math.AP↗

arXiv2024

Optimal design of equilibrium solutions of the Vlasov-Poisson system by an external electric field

A new optimization framework to design steady equilibrium solutions of the Vlasov-Poisson system by means of external electric fields is presented. This optimization framework requires the minimization of an ensemble functional with Tikhonov regularization of the control field under the differential constraint of a nonlinear elliptic equation that models equilibrium solutions of the Vlasov-Poisson system. Existence of optimal control fields and their characterization as solutions to first-order optimality conditions are discussed. Numerical approximations and optimization schemes are developed to validate the proposed framework.

math.OC↗

arXiv2024

A hybrid Krasnosel'skiĭ-Schauder fixed point theorem for systems

We provide new results regarding the localization of the solutions of nonlinear operator systems. We make use of a combination of Krasnosel'ski\uı cone compression-expansion type methodologies and Schauder-type ones. In particular we establish a localization of the solution of the system within the product of a conical shell and of a closed convex set. By iterating this procedure we prove the existence of multiple solutions. We illustrate our theoretical results by applying them to the solvability of systems of Hammerstein integral equations. In the case of two specific boundary value problems and with given nonlinearities, we are also able to obtain a numerical solution, consistent with our theoretical results.

math.CA↗

arXiv2023

Forest fire spreading: a nonlinear stochastic model continuous in space and time

Forest fire spreading is a complex phenomenon characterized by a stochastic behavior. Nowadays, the enormous quantity of georeferenced data and the availability of powerful techniques for their analysis can provide a very careful picture of forest fires opening the way to more realistic models. We propose a stochastic spreading model continuous in space and time that is able to use such data in their full power. The state of the forest fire is described by the subprobability densities of the green trees and of the trees on fire that can be estimated thanks to data coming from satellites and earth detectors. The fire dynamics is encoded into a density probability kernel which can take into account wind conditions, land slope, spotting phenomena and so on, bringing to a system of integro-differential equations for the probability densities. Existence and uniqueness of the solutions is proved by using Banach's fixed point theorem. The asymptotic behavior of the model is analyzed as well. Stochastic models based on cellular automata can be considered as particular cases of the present model from which they can be derived by space and/or time discretization. Suggesting a particular structure for the kernel, we obtain numerical simulations of the fire spreading under different conditions. For example, in the case of a forest fire evolving towards a river, the simulations show that the probability density of the trees on fire is different from zero beyond the river due to the spotting phenomenon. Firefighters interventions and weather changes can be easily introduced into the model.

q-bio.PE↗