Control Problems for Conservation Laws with Traffic Applications
Modeling, Analysis, and Numerical Methods
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Chapter and Conference Paper
Hyperbolic Techniques in Epidemiological Modeling
We present a class of models devoted to the spreading of a virus, inspired by the recent pandemics. Key features are the ability to comprehend age structure, spatial movements, social distancing policies and t...
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Article
Open AccessSwitched hyperbolic balance laws and differential algebraic equations
Motivated by several applications, we investigate the well-posedness of a switched system composed by a system of linear hyperbolic balance laws and by a system of linear algebraic differential equations. This...
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Article
Open AccessInfectious Disease Spreading Fought by Multiple Vaccines Having a Prescribed Time Effect
We propose a framework for the description of the effects of vaccinations on the spreading of an epidemic disease. Different vaccines can be dosed, each providing different immunization times and immunization ...
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Chapter
Introduction
This book focuses on control problems for conservation laws, i.e., equations of the type: ...
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Chapter
Lagrangian Control of Conservation Laws and Mixed Models
A vehicle with different (eventually controlled) dynamics from general traffic along a street may reduce the road capacity, thus generating a moving bottleneck, and can be used to act on the traffic flow. The int...
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Book
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Chapter
Boundary Control of Conservation Laws Exhibiting Shocks
This chapter focuses on control of systems of conservation laws with boundary data. Problems with one or two boundaries are considered and, in particular, we focus on cases where shocks may be developed by the...
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Chapter
Distributed Control for Conservation Laws
This chapter focuses on control of systems of conservation laws with distributed parameters. Problem with different parameterized fluxes is addressed: in particular, we deal with cases where the control is the...
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Chapter
Control Problems for Hamilton-Jacobi Equations Co-authored by Alexander Keimer
In this chapter, we introduce Hamilton-Jacobi PDEs. These PDEs are related to conservation laws and their solutions are the anti-derivative (in space) of the Entropy solutions of the corresponding conservation...
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Chapter
Decentralized Control of Conservation Laws on Graphs
Conservation and/or balance laws on networks in the recent years have been the subject of intense study, since a wide range of different applications in real life can be covered by such a research.
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Article
Well Posedness and Control in a NonLocal SIR Model
SIR models, also with age structure, can be used to describe the evolution of an infectious disease. A vaccination campaign influences this dynamics immunizing part of the susceptible individuals, essentially tur...
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Article
Open AccessAn age and space structured SIR model describing the Covid-19 pandemic
We present an epidemic model capable of describing key features of the Covid-19 pandemic. While capturing several qualitative properties of the virus spreading, it allows to compute the basic reproduction numb...
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Chapter
Crowd Dynamics Through Conservation Laws
We consider several macroscopic models, based on systems of conservation laws, for the study of crowd dynamics. All the systems considered here contain nonlocal terms, usually obtained through convolutions wit...
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Article
A mathematical model for piracy control through police response
We introduce a model describing the dynamics and interactions of three populations of ships (pirates ships, commercial cargos, and police watercrafts) in a marine region. We establish well-posedness of the cou...
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Article
Boundary coupling of microscopic and first order macroscopic traffic models
We couple, at a fixed interface, the microscopic Follow the Leader model and the macroscopic Lighthill–Whitham–Richards model, both used for describing vehicular traffic. The coupling is obtained by suitable b...
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Article
Optimal control in renewable resources modeling
A system of renewal equations on a graph provides a framework to describe the exploitation of a biological resource. In this context, we formulate an optimal control problem, prove the existence of an optimal ...
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Article
Differential Equations Modeling Crowd Interactions
Nonlocal conservation laws are used to describe various realistic instances of crowd behaviors. First, a basic analytic framework is established through an ad hoc well-posedness theorem for systems of nonlocal...
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Chapter
A Multibuffer Model for LWR Road Networks
This paper introduces a new model for describing intersections in road networks, whose load dynamics is governed by the Lighthill–Whitham–Richards model. More precisely we define a solution for intersections u...
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Chapter and Conference Paper
Conservation Laws at A Node
This survey paper deals with a system of conservation laws on a network composed by a single node with n incoming and m outgoing arcs. We analyze the Cauchy problem in the case of the Lighthill-Whitham-Richards (...
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Chapter and Conference Paper
A Fluidodynamic Model for Traffic in a Road Network
This paper is concerned with a fluidodynamic model for traffic flow. More precisely, we consider a single conservation law, deduced from the conservation of the number of cars, defined on a road network that i...
