The damped wave equation with unbounded damping

0489299 - ÚJF 2019 RIV US eng J - Journal Article
Freitas, P. - Siegl, Petr - Tretter, C.
The damped wave equation with unbounded damping.
Journal of Differential Equations. Roč. 264, č. 12 (2018), s. 7023-7054. ISSN 0022-0396. E-ISSN 1090-2732
Institutional support: RVO:61389005
Keywords : damped wave equation * unbounded damping * essential spectrum * quadratic operator funciton with unbounded coefficients * Schrodinger operators with complex potentials
OECD category: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Impact factor: 1.938, year: 2018

We analyze new phenomena arising in linear damped wave equations on unbounded domains when the damping is allowed to become unbounded at infinity. We prove the generation of a contraction semigroup, study the relation between the spectra of the semigroup generator and the associated quadratic operator function, the convergence of non-real eigenvalues in the asymptotic regime of diverging damping on a subdomain, and we investigate the appearance of essential spectrum on the negative real axis. We further show that the presence of the latter prevents exponential estimates for the semigroup and turns out to be a robust effect that cannot be easily canceled by adding a positive potential. These analytic results are illustrated by examples.
Permanent Link: http://hdl.handle.net/11104/0283744