Geodesic
On a differential game in an abstract parabolic system
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 2, pp. 26-40

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We consider the game problem of approach for a system whose dynamics is described by a differential operator equation in a Hilbert space. The equation is written in an implicit form with generally non-invertible operator multiplying the derivative. It is assumed that the characteristic operator pencil corresponding to the linear part of the equation satisfies a constraint of parabolic type in a right half-plane. Using the method of resolving functionals, we obtain sufficient conditions for the approach of a dynamical vector of the system to a cylindrical terminal set. Applications to systems described by partial differential equations are considered.
Keywords: differential game, parabolic system, ergodic theorem, pseudoresolvent, generator of a semigroup, set-valued mapping, resolving functional, partial differential equation. 
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L. A. Vlasenko; A. G. Rutkas; A. A. Chikrii. On a differential game in an abstract parabolic system. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 2, pp. 26-40. http://geodesic.mathdoc.fr/item/TIMM_2015_21_2_a2/