On a differential game in a nondamped distributed system. (English) Zbl 1432.49053
Summary: We study a differential game of approach in a system whose dynamics is described by a Sobolev-type second-order operator differential equation in Hilbert spaces. Solutions of the equation are represented by cosine and sine operator functions. To obtain solvability conditions of the game problem, we use support functionals of two sets, which defined by the behaviors of pursuer and evader. The results are applied to the investigation of conflicted-controlled dynamics of bending waves in a rod.
MSC:
| 49N70 | Differential games and control |
| 91A23 | Differential games (aspects of game theory) |
| 47D09 | Operator sine and cosine functions and higher-order Cauchy problems |
| 49N75 | Pursuit and evasion games |
| 35Q74 | PDEs in connection with mechanics of deformable solids |
| 74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
Keywords:
cosine and sine operator functions; differential game of approach; mathematical model of bending waves in a rod; partial differential equation; pursuer and evader; Sobolev differential equation; support functionalReferences:
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