Dynamic blocking problems for a model of fire propagation

Research output: Chapter in Book/Report/Conference proceedingChapter

4 Citations (Scopus)

Abstract

This paper contains a survey of recent work on a class of dynamic blocking problems. The basic model consists of a differential inclusion describing the growth of a set in the plane. To restrain its expansion, it is assumed that barriers can be constructed, in real time. Here the issues of major interest are: (i) whether the growth of the set can be eventually blocked, and (ii) what is the optimal location of the barriers, minimizing a cost criterion. After introducing the basic definitions and concepts, the paper reviews various results on the existence or non-existence of blocking strategies. A theorem on the existence of an optimal strategy is then recalled, together with various necessary conditions for optimality. Sufficient conditions for optimality and a numerical algorithm for the computation of optimal barriers are also discussed, together with several open problems.

Original languageEnglish (US)
Title of host publicationAdvances in Applied Mathematics, Modeling, and Computational Science
EditorsRoderick Melnik
Pages11-40
Number of pages30
DOIs
StatePublished - Mar 1 2013

Publication series

NameFields Institute Communications
Volume66
ISSN (Print)1069-5265

Fingerprint

Propagation
Optimality
Optimal Location
Differential Inclusions
Optimal Strategy
Numerical Algorithms
Nonexistence
Open Problems
Model
Necessary Conditions
Sufficient Conditions
Costs
Theorem
Concepts
Class
Review
Strategy

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Bressan, A. (2013). Dynamic blocking problems for a model of fire propagation. In R. Melnik (Ed.), Advances in Applied Mathematics, Modeling, and Computational Science (pp. 11-40). (Fields Institute Communications; Vol. 66). https://doi.org/10.1007/978-1-4614-5389-5_2
Bressan, Alberto. / Dynamic blocking problems for a model of fire propagation. Advances in Applied Mathematics, Modeling, and Computational Science. editor / Roderick Melnik. 2013. pp. 11-40 (Fields Institute Communications).
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Bressan, A 2013, Dynamic blocking problems for a model of fire propagation. in R Melnik (ed.), Advances in Applied Mathematics, Modeling, and Computational Science. Fields Institute Communications, vol. 66, pp. 11-40. https://doi.org/10.1007/978-1-4614-5389-5_2

Dynamic blocking problems for a model of fire propagation. / Bressan, Alberto.

Advances in Applied Mathematics, Modeling, and Computational Science. ed. / Roderick Melnik. 2013. p. 11-40 (Fields Institute Communications; Vol. 66).

Research output: Chapter in Book/Report/Conference proceedingChapter

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Bressan A. Dynamic blocking problems for a model of fire propagation. In Melnik R, editor, Advances in Applied Mathematics, Modeling, and Computational Science. 2013. p. 11-40. (Fields Institute Communications). https://doi.org/10.1007/978-1-4614-5389-5_2