Sets invariant under an integral constraint on controls

2011

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DOI 10.3103/s1066369x11080093
Data confidence 70 medium
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Abstract

In this paper we study the invariance of given sets with respect to a system with distributed parameters. The considered system is described by a heat conductivity equation whose right-hand side written in the additive form contains a control. For the initial data we obtain sufficient conditions for the strong and weak invariance of the set that represents the graph of a given multivalued mapping.