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Second microlocalization and stabilization of damped wave equations on tori. (English) Zbl 1383.35008
Colombini, Ferruccio (ed.) et al., Shocks, singularities and oscillations in nonlinear optics and fluid mechanics. Papers based on the workshop, Rome, Italy, September 2015. Cham: Springer (ISBN 978-3-319-52041-4/hbk; 978-3-319-52042-1/ebook). Springer INdAM Series 17, 55-73 (2017).
In this paper, the author gives a simple necessary and sufficient geometric condition on two dimensional tori for uniform stabilization in the special case when the damping \(a\) is a linear combination of characteristic functions of polygons.
For the entire collection see [Zbl 1371.76002].

MSC:
35A27 Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs
58J45 Hyperbolic equations on manifolds
35B40 Asymptotic behavior of solutions to PDEs
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