JournalszaaVol. 22, No. 1pp. 167–178

Exponential Growth for a Fractionally Damped Wave Equation

  • Nasser-edine Tatar

    King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia
  • Mokhtar Kirane

    Université de la Rochelle, France
Exponential Growth for a Fractionally Damped Wave Equation cover
Download PDF

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