Exponential decay for a locally damped fifth-order equation posed on the line. (August 2016) - Doronin, G.G.; Natali, F.
Abstract: We prove the exponential decay of the energy related to a locally damped fifth-order equation posed on the whole real line with the initial datum from a bounded set of L 2 . A local smoothing effect in H 2 is established, which is essential to obtain the necessary a priory estimates. Moreover, it is shown that arguments used in the article can be applied to prove the exponential decay rate of solutions for the Korteweg–de Vries equation with a similar localized damping term provided the initial data are uniformly bounded in L 2 . This last fact improves some previous results.