Instability results for the damped wave equation in unbounded domains

Details Instability results for the damped wave equation in unbounded domains Instability results for the damped wave equation in unbounded domains

2004-06-02

arxiv.org/abs/math/0406041v1

J. Differential Equations 211 (2005), no. 1, 168-186.

Mathematics

Analysis of PDEs

LaTeX, 19 pages; to appear in J. Differential Equations

Scientific paper

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 $\alpha$. In order to prove these results, we generalize some existing results on the asymptotic behaviour of eigencurves of one-parameter families of Schrodinger operators to the unbounded case, which we believe to be of interest in their own right.

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