Wave propagation in abstract dynamical system with boundary control

2023/07/02 by Μ. I. Belishev, Belishev, M. I. · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Differential Equations and Boundary Problems #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2307.00605

openalex publication_date 2023/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let L₀ be a positive definite operator in a Hilbert space \mathscr H with the defect indexes n_±\geqslant 1 and let \\rm Ker L^*₀;Γ₁,Γ₂\ be its canonical (by M.I.Vishik) boundary triple. The paper deals with an evolutionary dynamical system of the form amp; u_tt+L₀^* u=0 amp;amp;in \mathscr H, tgt;0;
amp; u|_t=0=u_t|_t=0=0 amp;amp; \rm in \mathscr H;
amp; Γ₁ u=f(t), amp;amp; t\geqslant 0, 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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