An improved exponential decay result for some semilinear integrodifferential equations

S. Mazouzi and N.-E. Tatar

Departement de Mathematiques, Universite Badji Mokhtar,
BP 12, Annaba, 23000,  Algeria.

King Fahd University of Petroleum and Minerals,
Department of Mathematical Sciences,
31261 Dhahran, Saudi Arabia.


We prove exponential decay for the solution of an abstract integrodifferential equation.
This equation involves coefficients of polynomial type, weakly singular kernels as well
as different powers of the unknown in some norms.

AMSclassification. 35R10.

Keywords. Semigroup, fractional operator, weakly singular kernels, exponential decay.