Differential and Integral Equations

Polynomial decay to a class of abstract coupled systems with past history

D.S.A. Júnior, L.P.V. Matos, and M.L. Santos

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We consider a class of coupled systems with past history acting only in one equation. We show in the abstract setting that the dissipation given by the history term is not strong enough to produce exponential stability. We show that the solution decays polynomially to zero, with rates that can be improved depending on the regularity of the initial data. Some examples are given.

Article information

Differential Integral Equations, Volume 25, Number 11/12 (2012), 1119-1134.

First available in Project Euclid: 20 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35B40: Asymptotic behavior of solutions 35L70: Nonlinear second-order hyperbolic equations


Matos, L.P.V.; Júnior, D.S.A.; Santos, M.L. Polynomial decay to a class of abstract coupled systems with past history. Differential Integral Equations 25 (2012), no. 11/12, 1119--1134. https://projecteuclid.org/euclid.die/1356012253

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