Filippov and invariance theorems for mutational inclusions of tubes
Doyen, Luc (1993), Filippov and invariance theorems for mutational inclusions of tubes, Set-Valued Analysis, 1, 3, p. 289-303. http://dx.doi.org/10.1007/BF01027639
TypeArticle accepté pour publication ou publié
Journal nameSet-Valued Analysis
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Abstract (EN)The framework of transitions and mutational calculus inspired by shape optimization allows the notions of derivative, tangent cone, and differential equation to be extended to a metric space and especially to the family of all nonempty compact subsets of a given domainE. It gives tools to study the evolution of tubes and fundamental theorems such as those of Cauchy-Lipschitz, Nagumo, or Lyapunov, well known in vector spaces, can be adapted to mutational equations. The present paper deals with mutational inclusions of tubes which include many tube control problems and an adaptation of the Filippov theorem is proved. As a consequence, an invariance theorem is stated.
Subjects / KeywordsTransitions; mutations; Filippov's theorem; invariance; contingent cone
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