Exponential Growth for a Fractionally Damped Wave Equation
Nasser-edine Tatar
King Fahd University of Petroleum and Minerals, Dhahran, Saudi ArabiaMokhtar Kirane
Université de la Rochelle, France
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Abstract
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.
Cite this article
Nasser-edine Tatar, Mokhtar Kirane, Exponential Growth for a Fractionally Damped Wave Equation. Z. Anal. Anwend. 22 (2003), no. 1, pp. 167–178
DOI 10.4171/ZAA/1137