Geodesic
On a~differential game in a~distributed system
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 4, pp. 71-80

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We consider the game problem of approach for a system whose dynamics is described by a partial differential equation not of Kovalevskaya type, that is not solved in time derivative. In a Hilbert function space, the equation with boundary conditions are written in an abstract form as a differential operator equation. Using the method of resolving functionals, we obtain sufficient conditions for the approach of a dynamical vector of system to a cylindrical terminal set. Results are exemplified by means of a model problem concerning filtering fluids in fractured-porous rocks.
Keywords: differential game, set-valued mapping, resolving functional, partial differential equation, operator. 
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L. A. Vlasenko; A. A. Chikrii. On a~differential game in a~distributed system. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 4, pp. 71-80. http://geodesic.mathdoc.fr/item/TIMM_2014_20_4_a6/