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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Abstract

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

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

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356012253

Mathematical Reviews number (MathSciNet)
MR3013406

Zentralblatt MATH identifier
1274.35024

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

Citation

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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