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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.

An Epidemic Model With Post-Contact Prophylaxis of Distributed Length II. Stability and Oscillations if Treatment is Fully Effective

H. R. Thieme, A. Tridane, Y. Kuang (2008)

Mathematical Modelling of Natural Phenomena

A possible control strategy against the spread of an infectious disease is the treatment with antimicrobials that are given prophylactically to those that had contact with an infective person. The treatment continues until recovery or until it becomes obvious that there was no infection in the first place. The model considers susceptible, treated uninfected exposed, treated infected, (untreated) infectious, and recovered individuals. The overly optimistic assumptions are made that treated uninfected...

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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