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Zeitschrift für Analysis und ihre Anwendungen

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Volume 22, Issue 3, 2003, pp. 609–617
DOI: 10.4171/ZAA/1165

Published online: 2003-09-30

A Wave Equation with Fractional Damping

Nasser-edine Tatar[1]

(1) King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia

We consider a wave equation with an internal damping represented by a fractional derivative of lower order than one. An exponential growth result is proved in presence of a source of polynomial type. This result improves an earlier one where the initial data are supposed to be very large in some norm. A new argument based on a new functional is proposed.

Keywords: Exponential growth, fractional derivative, internal damping

Tatar Nasser-edine: A Wave Equation with Fractional Damping. Z. Anal. Anwend. 22 (2003), 609-617. doi: 10.4171/ZAA/1165