A stability result for a class of nonlinear integrodifferential equations with $L^1$ kernels
Volume 35 / 2008
Applicationes Mathematicae 35 (2008), 395-430
MSC: 45N05, 45M10, 93D20, 35L70.
DOI: 10.4064/am35-4-2
Abstract
We study second order nonlinear integro-differential equations in Hilbert spaces with weakly singular convolution kernels obtaining energy estimates for the solutions, uniform in $t$. Then we show that the solutions decay exponentially at $\infty $ in the energy norm. Finally, we apply these results to a problem in viscoelasticity.
