Geodesic
Sets invariant under an integral constraint on controls
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2011), pp. 69-76

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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.
Keywords: control, weak invariance, strong invariance, concentrated parameters. 
@article{IVM_2011_8_a8,
     author = {M. Tukhtasinov and U. Ibragimov},
     title = {Sets invariant under an integral constraint on controls},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {69--76},
     publisher = {mathdoc},
     number = {8},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2011_8_a8/}
}
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M. Tukhtasinov; U. Ibragimov. Sets invariant under an integral constraint on controls. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2011), pp. 69-76. http://geodesic.mathdoc.fr/item/IVM_2011_8_a8/