JournalszaaVol. 22 , No. 1DOI 10.4171/zaa/1137

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

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.