The EMS Publishing House is now EMS Press and has its new home at

Please find all EMS Press journals and articles on the new platform.

Zeitschrift für Analysis und ihre Anwendungen

Full-Text PDF (142 KB) | Metadata | Table of Contents | ZAA summary
Volume 22, Issue 1, 2003, pp. 167–178
DOI: 10.4171/ZAA/1137

Published online: 2003-03-31

Exponential Growth for a Fractionally Damped Wave Equation

Mokhtar Kirane[1] and Nasser-edine Tatar[2]

(1) Université de la Rochelle, France
(2) King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia

We consider a nonlinear wave equation with an internal damping represented by a fractional time derivative and with a polynomial source. It is proved that the solution is unbounded and grows up exponentially in the Lp-norm for sufficiently large initial data. To this end we use some techniques based on Fourier transforms and some inequalities such as the Hardy-Littlewood inequality.

Keywords: Exponential growth, fractional derivative, internal damping

Kirane Mokhtar, Tatar Nasser-edine: Exponential Growth for a Fractionally Damped Wave Equation. Z. Anal. Anwend. 22 (2003), 167-178. doi: 10.4171/ZAA/1137