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Polynomial Decay of Solutions to the Cauchy Problem for a Petrovsky–Petrovsky System in R n $\mathbb{R}^{n}$

Polynomial Decay of Solutions to the Cauchy Problem for a Petrovsky–Petrovsky System in R n... This paper describes a polynomial decay rate of solution for a coupled system of Petrovsky equations in R n $\mathbb{R}^{n}$ with infinite memory acting in the first equation. The weighted spaces and results in Guesmia (Appl. Anal. 94(1):184–217, 2015) are also used. The main contributions here is to show that the infinite memory lets our problem still dissipative and that the system is not exponentially stable in spite of the kernel in the memory term is sub-exponential. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

Polynomial Decay of Solutions to the Cauchy Problem for a Petrovsky–Petrovsky System in R n $\mathbb{R}^{n}$

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References (18)

Publisher
Springer Journals
Copyright
Copyright © 2016 by Springer Science+Business Media Dordrecht
Subject
Mathematics; Mathematics, general; Computer Science, general; Theoretical, Mathematical and Computational Physics; Complex Systems; Classical Mechanics
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/s10440-016-0058-1
Publisher site
See Article on Publisher Site

Abstract

This paper describes a polynomial decay rate of solution for a coupled system of Petrovsky equations in R n $\mathbb{R}^{n}$ with infinite memory acting in the first equation. The weighted spaces and results in Guesmia (Appl. Anal. 94(1):184–217, 2015) are also used. The main contributions here is to show that the infinite memory lets our problem still dissipative and that the system is not exponentially stable in spite of the kernel in the memory term is sub-exponential.

Journal

Acta Applicandae MathematicaeSpringer Journals

Published: Jul 19, 2016

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