Geodesic
Wave propagation in abstract dynamical system with boundary control
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 53, Tome 521 (2023), pp. 8-32 
M. I. Belishev. Wave propagation in abstract dynamical system with boundary control. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 53, Tome 521 (2023), pp. 8-32. http://geodesic.mathdoc.fr/item/ZNSL_2023_521_a1/
@article{ZNSL_2023_521_a1,
     author = {M. I. Belishev},
     title = {Wave propagation in abstract dynamical system with boundary control},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {8--32},
     year = {2023},
     volume = {521},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2023_521_a1/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Let $L_0$ be a positive definite operator in a Hilbert space $\mathscr H$ with the defect indexes $n_\pm\geqslant 1$ and let $\{{\rm Ker }L^*_0;\Gamma_1,\Gamma_2\}$ be its canonical (by M. I. Vishik) boundary triple. The paper deals with an evolutionary dynamical system of the form \begin{align*} & u_{tt}+{L_0^*} u=0 &&\text{in}\quad {\mathscr H}, t>0;\\ & u\big|_{t=0}=u_t\big|_{t=0}=0 && {\rm in }\quad {\mathscr H};\\ & \Gamma_1 u=f(t), && t\geqslant 0, \end{align*} where $f$ is a boundary control (a ${\rm Ker }L^*_0$-valued function of time), $u=u^f(t)$ is a trajectory. Some of the general properties of such systems are considered. An abstract analog of the finiteness principle of wave propagation speed is revealed.

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