A multidimensional Lyapunov type theorem
Solutions of lower semicontinuous differential inclusions on closed sets
Nonexistence of solutions for differential inclusions with upper semicontinuous nonconvex right-hand side
A lemma and a conjecture on the cost of rearrangements
On differential systems with impulsive controls
An ill posed Cauchy problem for a hyperbolic system in two space dimensions
On the well posedness of vanishing viscosity limits
This paper provides a survey of recent results concerning the stability and convergence of viscous approximations, for a strictly hyperbolic system of conservation laws in one space dimension. In the case of initial data with small total variation, the vanishing viscosity limit is well defined. It yields the unique entropy weak solution to the corresponding hyperbolic system.
From optimal control to non-cooperative differential games: a homotopy approach
A locally contractive metric for systems of conservation laws
Leggi di conservazione
Sistemi iperbolici di leggi di conservazione
This survey paper provides a brief introduction to the mathematical theory of hyperbolic systems of conservation laws in one space dimension. After reviewing some basic concepts, we describe the fundamental theorem of Glimm on the global existence of BV solutions. We then outline the more recent results on uniqueness and stability of entropy weak solutions. Finally, some major open problems and research directions are discussed in the last section.
Some remarks on multidimensional systems of conservation laws
This note is concerned with the Cauchy problem for hyperbolic systems of conservation laws in several space dimensions. We first discuss an example of ill-posedness, for a special system having a radial symmetry property. Some conjectures are formulated, on the compactness of the set of flow maps generated by vector fields with bounded variation.
Hyperbolic systems of conservation laws.
This is a survey paper, written in the occasion of an invited talk given by the author at the Universidad Complutense in Madrid, October 1998. Its purpose is to provide an account of some recent advances in the mathematical theory of hyperbolic systems of conservation laws in one space dimension. After a brief review of basic concepts, we describe in detail the method of wave-front tracking approximation and present some of the latest results on uniqueness and stability of entropy weak solutions....
Sulla funzione tempo minimo nei sistemi non lineari
Conditions for the continuity of the Minimal Time Function in the whole space are given; we prove also a theorem on local differentiability that generalizes some results previously obtained in the linear case.
Patchy vector fields and asymptotic stabilization
Selections and representations of multifunctions in paracompact spaces
Let (X,T) be a paracompact space, Y a complete metric space, a lower semicontinuous multifunction with nonempty closed values. We prove that if is a (stronger than T) topology on X satisfying a compatibility property, then F admits a -continuous selection. If Y is separable, then there exists a sequence of -continuous selections such that for all x ∈ X. Given a Banach space E, the above result is then used to construct directionally continuous selections on arbitrary subsets of ℝ × E.
On total differential inclusions
A maximum principle for optimally controlled systems of conservation laws
Nash equilibria for a model of traffic flow with several groups of drivers
Traffic flow is modeled by a conservation law describing the density of cars. It is assumed that each driver chooses his own departure time in order to minimize the sum of a departure and an arrival cost. There are groups of drivers, The -th group consists of drivers, sharing the same departure and arrival costs (), (). For any given population sizes ,, , we prove the existence of a Nash equilibrium solution, where no...
Stability rates for patchy vector fields
This paper is concerned with the stability of the set of trajectories of a patchy vector field, in the presence of impulsive perturbations. Patchy vector fields are discontinuous, piecewise smooth vector fields that were introduced in Ancona and Bressan (1999) to study feedback stabilization problems. For patchy vector fields in the plane, with polygonal patches in generic position, we show that the distance between a perturbed trajectory and an unperturbed one is of the same order of magnitude...
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