David Krejcirik (Instituto Superior Tecnico, Lisboa):

This is a joint work with Pedro Freitas. A preprint is available on:


``Instability results for the damped wave equation in unbounded domains"


We extend some previous results for the damped wave equation in bounded domains in Euclidean spaces to the unbounded case. In particular, we show that if the damping term is of the form $\alpha a$ with bounded $a$ taking on negative values on a set of positive measure, then there will always exist unbounded solutions for sufficiently large positive~$\alpha$. The instability result is obtained by relating the real part of the spectrum of the (non-self-adjoint) infinitesimal generator of the damped wave equation with the spectrum of a family of self-adjoint Schr\"odinger operators.

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Updated: May 4, 2004