A stability result for a class of nonlinear
 integrodifferential equations with $L^1$ kernels

Piermarco Cannarsa; Daniela Sforza

doi:10.4064/am35-4-2

Geodesic

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A stability result for a class of nonlinear integrodifferential equations with $L^1$ kernels

Piermarco Cannarsa ¹ ; Daniela Sforza ²

¹ Dipartimento di Matematica Università di Roma Tor Vergata Via della Ricerca Scientifica 1 00133 Roma, Italy
² Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate Università di Roma La Sapienza Via A. Scarpa 16 00161 Roma, Italy

Applicationes Mathematicae, Tome 35 (2008) no. 4, pp. 395-430.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Résumé

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.

DOI : 10.4064/am35-4-2

Keywords: study second order nonlinear integro differential equations hilbert spaces weakly singular convolution kernels obtaining energy estimates solutions uniform solutions decay exponentially infty energy norm finally apply these results problem viscoelasticity

Affiliations des auteurs :

Piermarco Cannarsa ¹ ; Daniela Sforza ²

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Piermarco Cannarsa; Daniela Sforza. A stability result for a class of nonlinear
 integrodifferential equations with $L^1$ kernels. Applicationes Mathematicae, Tome 35 (2008) no. 4, pp. 395-430. doi : 10.4064/am35-4-2. http://geodesic.mathdoc.fr/articles/10.4064/am35-4-2/

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