Spreadability and evolving interfaces

Bernoussi, Abdes Samed; Jai, A. El; Pritchard, A. J.

doi:10.1080/00207720110035246

Cited by 10 publications

(9 citation statements)

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“…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].…”

Section: Proposition 3 (S) Is A-spreadable (Respectively A-resorbablmentioning

confidence: 99%

“…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).…”

Section: Introductionmentioning

confidence: 99%

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Spreadability, Vulnerability and Protector Control

Bernoussi¹

2010

Math. Model. Nat. Phenom.

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Section: Proposition 3 (S) Is A-spreadable (Respectively A-resorbablmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Spreadability, Vulnerability and Protector Control

Bernoussi¹

2010

Math. Model. Nat. Phenom.

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“…For that purpose, we recall the following definition (Bernoussi and El Jai, 2000;Bernoussi et al, 2001).…”

Section: 13mentioning

confidence: 99%

“…The choice of D as the determination of the adapted family of transformations remains very difficult. However, it is possible, for some class of systems such as transportation ones or those which evolve as a travelling wave, to determine such families (Bernoussi et al, 2001). Then, based on the principle of this second approach as well as Definitions 1 and 2, the protection of σ can be characterized as in the following result.…”

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confidence: 99%

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Protector control: Extension to a class of nonlinear distributed systems

Qaraai¹,

Bernoussi²

2010

International Journal of Applied Mathematics and Computer Science

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We present an extension of the protector control scheme introduced for the linear case in a previous work to a class of nonlinear systems. The systems considered are assumed to have a finite propagation velocity while the initial state is subject to a spreading disturbance. We characterize such a control first by using the remediability approach to the resulting nonlinear delay system, and then by coupling families of transformations and the delay approach. To illustrate this work, we provide a simulation example.

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Analyse régionale des systèmes distribués

Jai

2002

ESAIM: COCV

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Abstract. The aim of this paper is to give the state of the art in the regional analysis of distributed parameter systems. The statement of regional analysis problems is: given a dynamical system defined on a domain Ω, one focuses the study of its controllability, its observability, its stability, ... only on a given subregion ω, ω ⊂ Ω. We develop the extension of classical concepts as well as new concepts like spreadability. Various results and examples illustrate the paper.Résumé. Le but de cet article est de montrer l'état de l'art dans l'analyse des systèmes distribués lorsque l'on examine certains conceptsà partir de considérations régionales. Autrement dit,à partir de la donnée d'un système dynamique défini sur un domaine Ω, on ne s'intéresseà sa contrôlabilité, a son observabilité,à sa stabilité, ... que sur une région privilégiée ω, ω ⊂ Ω. Partant de concepts classiques, on développe leur adaptation au cas régional. On développe ensuite des concepts régionaux propres aux systèmes distribués tels que l'étalabilité. Divers développements spécifiques sont donnés. De nombreux résultats et exemples illustrent le travail.Classification Mathématique. 93C20.

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Spreadability and evolving interfaces

Cited by 10 publications

References 10 publications

Spreadability, Vulnerability and Protector Control

Spreadability, Vulnerability and Protector Control

Protector control: Extension to a class of nonlinear distributed systems

Analyse régionale des systèmes distribués

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