We consider the wave equation in a bounded region with a smooth boundary with distributed delay on the boundary or into the domain. In both cases, under suitable assumptions, we prove the expo- nential stability of the solution. These results are obtained by introduc- ing suitable energies and by proving some observability inequalities. For an internal distributed delay, we further show some instability results.
Stabilization of the wave equation with boundary or internal distributed delay
PIGNOTTI, CRISTINA
2008-01-01
Abstract
We consider the wave equation in a bounded region with a smooth boundary with distributed delay on the boundary or into the domain. In both cases, under suitable assumptions, we prove the expo- nential stability of the solution. These results are obtained by introduc- ing suitable energies and by proving some observability inequalities. For an internal distributed delay, we further show some instability results.File in questo prodotto:
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