New approach of spreadability

Spreadability, Vulnerability and Protector Control

“…To characterize the A-spreadability, A. Bernoussi and A. El Jai [4] have introduced a family of transformations which permit to describe the space evolution of the subdomain w t = {x ∈ Ω : Pz(x, t)}. We recall the following definition [4] in the case of null spreadability.…”

“…In both cases it can reach σ. We have the following characterization: (F (., s, t)) adapted to the evolution of (S) and t 1 ∈ I such that: For more details about spreadability see [4,5,8,9] and vulnerability [3,6]. An application to the groundwater pollution is given in [2].…”

“…More particularly, to describe some environmental phenomena such as pollution, epidemics or fires of forests and so on. The concept of spreadability was introduced by A. El Jai and K. Kassara [7] and developed by A. Bernoussi and A. El Jai [4,5]. Later the concept of vulnerability was introduced by A. Bernoussi and M. Amharref [6], [3] in order to characterize the zones which can be reached by a given property P (pollution for example).…”

Protector control: Extension to a class of nonlinear distributed systems

“…For that purpose, we use the concept of spreadability (El Jai and Kassara, 1994;1996;Bernoussi and El Jai, 2000;Bernoussi et al, 2001). Hence, this leads to the problem of the influence of this disturbance on some given areas, and also the possibility of subjecting them to controls to achieve some specified objectives.…”

“…Qaraai and A.S. Bernoussi concerns the so-called adaptable families of transformations used to characterize the spreadability of the system considered (Bernoussi and El Jai, 2000), while the other is based on regional remediability not for the original system but for some suitable delay system. A common aspect of these two approaches is to deviate the property generated by the disturbance effects for not passing into a given vulnerable zone.…”