Zeitschrift für Analysis und ihre Anwendungen
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Published online: 2003-03-31
Exponential Growth for a Fractionally Damped Wave EquationMokhtar Kirane and Nasser-edine Tatar (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