Null-controllability properties of the wave equation with a second order\n memory term

2018/07/09 by Umberto Biccari, Biccari, Umberto, Sorin Micu +1
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1807.03035

openalex publication_date 2018/07/09 · openalex created_date 2022/08/04 · openalex updated_date 2026/07/28

Abstract

We study the internal controllability of a wave equation with memory in the\nprincipal part, defined on the one-dimensional torus\n mathbbT=\ℝ/2\π\ℤ. We assume that the control is acting on\nan open subset \ω(t)\⊂ mathbbT, which is moving with a constant\nvelocity c\∈\ℝ\∖ -1,0,1 . The main result of the paper\nshows that the equation is null controllable in a sufficiently large time T\nand for initial data belonging to suitable Sobolev spaces. Its proof follows\nfrom a careful analysis of the spectrum associated to our problem and from the\napplication of the classical moment method.\n

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