Instability results for the damped wave equation in unbounded domains
Loading...
Date
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Description
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 $αa$ with bounded $a$ taking on negative values on a set of positive measure, then there will always exist unbounded solutions for sufficiently large positive $α$.
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.
LaTeX, 19 pages; to appear in J. Differential Equations
LaTeX, 19 pages; to appear in J. Differential Equations