Convergence of the regularized short pulse equation to the short pulse one

We consider the regularized short-pulse equation, which contains nonlinear dis- persive effects. We prove that as the diffusion parameter tends to zero, the solutions of the dispersive equation converge to discontinuous weak solutions of the short-pulse one. The proof relies on deriving suitable a priori estimates together with an application of the compensated compactness method in the Lp setting

Wellposedness results for the short pulse equation

The short pulse equation provides a model for the propagation of ultra-short light pulses in silica optical fibers. It is a nonlinear evolution equation. In this paper the wellposedness of bounded solutions for the homogeneous initial boundary value problem and the Cauchy problem associated to this equation are studied.Comment: arXiv admin note: text overlap with arXiv:1310.701

Convergence of the Ostrovsky equation to the Ostrovsky-Hunter one

We consider the Ostrovsky equation, which contains nonlinear dispersive effects. We prove that as the diffusion parameter tend to zero, the solutions of the dispersive equation converge to discontinuous weak solutions of the Ostrovsky-Hunter equation. The proof relies on deriving suitable a priori estimates together with an application of the compensated compactness method in the L^p setting

Oleinik type estimates for the Ostrovsky-Hunter eequation

The Ostrovsky-Hunter equation provides a model for small-amplitude long waves in a rotating fluid of finite depth. It is a nonlinear evolution equation. In this paper we study the well-posedness for the Cauchy problem associated to this equation within a class of bounded discontinuous solutions. We show that we can replace the Kruzkov-type entropy inequalities by an Oleinik-type estimate and prove uniqueness via a nonlocal adjoint problem. An implication is that a shock wave in an entropy weak solution to the Ostrovsky-Hunter equation is admissible only if it jumps down in value (like the inviscid Burgers equation)

Differential Calculus on Manifolds with a Boundary. Applications

This paper contains a set of lecture notes on manifolds with boundary and corners, with particular attention to the space of quantum states. A geometrically inspired way of dealing with these kind of manifolds is presented,and explicit examples are given in order to clearly illustrate the main ideas.Comment: 42 pages, 6 figures, accepted for publication in International Journal of Geometric Methods in Modern Physic

Cooperative sensing of spectrum opportunities

Reliability and availability of sensing information gathered from local spectrum sensing (LSS) by a single Cognitive Radio is strongly affected by the propagation conditions, period of sensing, and geographical position of the device. For this reason, cooperative spectrum sensing (CSS) was largely proposed in order to improve LSS performance by using cooperation between Secondary Users (SUs). The goal of this chapter is to provide a general analysis on CSS for cognitive radio networks (CRNs). Firstly, the theoretical system model for centralized CSS is introduced, together with a preliminary discussion on several fusion rules and operative modes. Moreover, three main aspects of CSS that substantially differentiate the theoretical model from realistic application scenarios are analyzed: (i) the presence of spatiotemporal correlation between decisions by different SUs; (ii) the possible mobility of SUs; and (iii) the nonideality of the control channel between the SUs and the Fusion Center (FC). For each aspect, a possible practical solution for network organization is presented, showing that, in particular for the first two aspects, cluster-based CSS, in which sensing SUs are properly chosen, could mitigate the impact of such realistic assumptions

La cultura dei servizi di accoglienza migranti in Italia. Una ricerca esplorativa [The culture of migrant reception services in Italy. An exploratory research]

Italy has a long history of immigration, which has become part of the country’s landscape in a complex and varied way, and has led to significant changes in important contexts such as in the school, the work place, and in the provision of welfare services. And yet, immigration policies still consist in emergency measures that do not recognize the phenomenon in its long -standing and structural dimension. In addition, public opinion is concerned as a result of the alarmist distortion of this issue, as shown by the gapbetween data on immigration and perceived immigration. Since in this research we take into consideration collusively shared experiences, these misunderstandings can not be corrected by providing more information on the real data; we posit that the emotional scope must be recognized in order to address this issue. In particular, we asked ourselves how this context -changes brought by immigration, public opinion, and government policies -is repre sented within the migrant Accordingly, we interviewed a group of reception staff from the Roman area on the type of service that they think they are offering. The results show how, in their experience, this complex reality of immigration is not evoked: the experience within the services is isolated from the Italian narrative and context. However, the voice of migrants and their point of view, emerge as a resource within these services, as openness rather than isolation

Well-posedness result for the Kuramoto–Velarde equation

AbstractThe Kuramoto–Velarde equation describes slow space-time variations of disturbances at interfaces, diffusion–reaction fronts and plasma instability fronts. It also describes Benard–Marangoni cells that occur when there is large surface tension on the interface in a microgravity environment. Under appropriate assumption on the initial data, of the time T, and the coefficients of such equation, we prove the well-posedness of the classical solutions for the Cauchy problem, associated with this equation