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A stability result for a class of nonlinear integrodifferential equations with L¹ kernels

Piermarco Cannarsa, Daniela Sforza (2008)

Applicationes Mathematicae

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.

Asymptotic behaviour of a transport equation

Ryszard Rudnicki (1992)

Annales Polonici Mathematici

We study the asymptotic behaviour of the semigroup of Markov operators generated by the equation u t + b u x + c u = a 0 a x u ( t , a x - y ) μ ( d y ) . We prove that for a > 1 this semigroup is asymptotically stable. We show that for a ≤ 1 this semigroup, properly normalized, converges to a limit which depends only on a.

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