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

Tom 35 / 2008

Piermarco Cannarsa, Daniela Sforza Applicationes Mathematicae 35 (2008), 395-430 MSC: 45N05, 45M10, 93D20, 35L70. DOI: 10.4064/am35-4-2

Streszczenie

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.

Autorzy

  • Piermarco CannarsaDipartimento di Matematica
    Università di Roma Tor Vergata
    Via della Ricerca Scientifica 1
    00133 Roma, Italy
    e-mail
  • Daniela SforzaDipartimento di Metodi e Modelli Matematici
    per le Scienze Applicate
    Università di Roma La Sapienza
    Via A. Scarpa 16
    00161 Roma, Italy
    e-mail

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