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Spreadability and vulnerability of distributed parameter systems. (English) Zbl 1115.93007

Summary: In this article we focus on the mathematical development of vulnerability concept and vulnerability index and analyze the dependence of the vulnerability concept definition on that of spreadability [A. El Jai and K. Kassara, Math. Comput. Modelling 20, No. 1, 47–64 (1994; Zbl 0829.92018); A. Bernoussi and A. El Jai, ibid. 31, 93–109 (2000; Zbl 0960.93018); A. Bernoussi, A. El Jai and A. J. Pritchard, Int. J. Syst. Sci. 32, No. 10, 1217–1232 (2001; Zbl 1014.93015)]. It is found that the mathematical approach of the vulnerability concept is rather attractive and can be applied to many engineering problems. To illustrate this, some examples and applications are considered.

MSC:

93A30 Mathematical modelling of systems (MSC2010)
93C20 Control/observation systems governed by partial differential equations
90B25 Reliability, availability, maintenance, inspection in operations research
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