Energy decay for a porous-elastic system with nonlinear localized damping
Tóm tắt
In this paper, we are considering the one-dimensional porous-elastic system with nonlinear localized damping acting in a arbitrary small region of the interval under consideration. Assuming appropriate assumptions on the nonlinear terms, we establish the energy decay of the corresponding system. To do this, we used the observability inequality obtained for the conservative system combined with a unique continuation property recently introduced in Ma et al. (Attractors for locally damped Bresse systems and a unique continuation property, 2021.
arXiv:2102.12025
) and the reduction principle (see Daloutli et al. in Discrete Contin Dyn Syst 2(1):67–94, 2009) where the problem of decay rates with nonlinear damping is reduced to an appropriate stabilizability inequality for the linear equation. This study generalizes and improves previous literature outcomes.
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