Abstract
The problem of boundary controllability is considered for a wide class of models, which can be conditionally called “naive mechanics”. It is proved that for all models of “naive mechanics”, except for the three cases, there is no controllability to rest. All these three cases are classical examples of equations, two of which require additional study of the controllability property.
Publisher
The Russian Academy of Sciences
Reference12 articles.
1. Gurtin M.E., Pipkin A.C. A general theory of heat conduction with finite wave speeds // Arch. Ration. Mech. Anal., 1968, no. 31, pp. 113–126.
2. Il’yushin A.A., Pobedrya B.E., Fundamentals of the Mathematical Theory of Thermoviscoelasticity. Moscow: Nauka, 1970. (in Russian)
3. Vlasov V.V., Rautian N.A., Shamaev A.S. Spectral analysis and correct solvability of abstract integro-differential equations arising in thermophysics and acoustics // Contemp. Math. Fundam. Direct., 2011, vol. 39, pp. 36–65.
4. Romanov I., Shamaev A. Exact controllability of the distributed system, governed by string equation with memory // J. Dyn.&Control Syst., 2013, vol. 19, no. 4, pp. 611–623.
5. Romanov I., Shamaev A. Exact control of a distributed system described by the wave equation with integral memory // J. Math. Sci., 2022, vol. 262, pp. 358–373.