David Krejcirik (Instituto
Superior Tecnico, Lisboa):
This is a joint work with Pedro Freitas.
A preprint is available on:
http://www.math.kth.se/spect/preprints/.
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``Instability
results for the damped wave equation in unbounded domains"
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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