Nonexistence of Solutions to a Hyperbolic Equation with a Time Fractional Damping
Nasser-edine Tatar
King Fahd University of Petroleum and Minerals, Dhahran, Saudi ArabiaMokhtar Kirane
Université de la Rochelle, France

Abstract
We consider the nonlinear hyperbolic equation \begin{align*} u_{tt}-\Delta u+D_{+}^{\alpha }u=h(t,x)\left| u\right| ^{p} \end{align*} posed in where , is a time fractional derivative, with given initial position and velocity and We find the Fujita's exponent which separates in terms of and the case of global existence from the one of nonexistence of global solutions. Then, we establish sufficient conditions on and assuring non-existence of local solutions.
Cite this article
Nasser-edine Tatar, Mokhtar Kirane, Nonexistence of Solutions to a Hyperbolic Equation with a Time Fractional Damping. Z. Anal. Anwend. 25 (2006), no. 2, pp. 131–142
DOI 10.4171/ZAA/1281