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On a differential game in a nondamped distributed system
Author(s) -
Rutkas Anatolii,
Vlasenko Larisa
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5712
Subject(s) - mathematics , sobolev space , trigonometric functions , differential game , pursuer , operator (biology) , hilbert space , mathematical analysis , differential equation , differential operator , mathematical optimization , biochemistry , chemistry , geometry , repressor , transcription factor , gene
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.