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 ∞ in the energy norm. Finally, we apply these results to a problem in viscoelasticity.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am35-4-2,
author = {Piermarco Cannarsa and Daniela Sforza},
title = {A stability result for a class of nonlinear integrodifferential equations with L$^1$ kernels},
journal = {Applicationes Mathematicae},
volume = {35},
year = {2008},
pages = {395-430},
zbl = {1163.45009},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am35-4-2}
}
Piermarco Cannarsa; Daniela Sforza. A stability result for a class of nonlinear integrodifferential equations with L¹ kernels. Applicationes Mathematicae, Tome 35 (2008) pp. 395-430. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am35-4-2/