Interior degenerate/singular parabolic equations in nondivergence form: well-posedness and Carleman estimates

We consider non smooth general degenerate/singular parabolic equations in non divergence form with degeneracy and singularity occurring in the interior of the spatial domain, in presence of Dirichlet or Neumann boundary conditions. In particular, we consider well posedness of the problem and then we prove Carleman estimates for the associated adjoint problem.Comment: Accepted in Journal of Differential Equations. arXiv admin note: text overlap with arXiv:1507.0778

The Propensity to Disruption for Evaluating a Parliament

The issue of power plays a relevant role in evaluating the representativeness of a Parliament. In this paper a new governability index is introduced, taking inspiration from the propensity to disruption and referring to the power of the parties.Electoral system, representativeness, governability, simulation

Stability of solutions to nonlinear wave equations with switching time-delay

In this paper we study well-posedness and asymptotic stability for a class of nonlinear second-order evolution equations with intermittent delay damping. More precisely, a delay feedback and an undelayed one act alternately in time. We show that, under suitable conditions on the feedback operators, asymptotic stability results are available. Concrete examples included in our setting are illustrated. We give also stability results for an abstract model with alternate positive-negative damping, without delay

Carleman estimates, observability inequalities and null controllability for interior degenerate non smooth parabolic equations

We show Carleman estimates, observability inequalities and null controllability results for parabolic equations with non smooth coefficients degenerating at an interior point.Comment: Accepted in Memoirs of the American Mathematical Societ

Strategic Manipulations and Collusions in Knaster Procedure

The Knaster’s procedure is one of the simplest and most powerful mechanisms for allocating indivisible objects among agents requiring them, but its sealed bid feature may induce some agents in altering their valuations. In this paper we study the consequences of false declarations on the agents’ payoffs. A misrepresentation of a single agent could produce a gain or a loss. So, we analyze a possible behavior of a subset of infinitely risk-averse agents and propose how to obtain a safe gain via a joint misreporting of their valuations, regardless of the declarations of the other agents.Knaster’s procedure, misrepresentation, collusion

Carleman estimates and null controllability for a degenerate population model

We deal with a degenerate model describing the dynamics of a population depending on time, on age and on space. We assume that the degeneracy can occur at the boundary or in the interior of the space domain and we focus on null controllability problem. To this aim, we prove first Carleman estimates for the associated adjoint problem, then, via cut off functions, we prove the existence of a null control function localized in the interior of the space domain

Carleman estimates for parabolic equations with interior degeneracy and Neumann boundary conditions

We consider a parabolic problem with degeneracy in the interior of the spatial domain and Neumann boundary conditions. In particular, we will focus on the well-posedness of the problem and on Carleman estimates for the associated adjoint problem. The novelty of the present paper is that for the first time it is considered a problem with an interior degeneracy and Neumann boundary conditions so that no previous result can be adapted to this situation. As a consequence new observability inequalities are established.Comment: Accepted in J. Anal. Math. arXiv admin note: text overlap with arXiv:1508.0401