Existence of global solutions and decay estimates for a viscoelastic Petrovsky equation with a delay term in the non-linear internal feedback

Date

2017-02-27

Authors

Mezouar, Nadia
Abdelli, Mama
Rachah, Amira

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Publisher

Texas State University, Department of Mathematics

Abstract

In this article we consider a nonlinear viscoelastic Petrovsky equation in a bounded domain with a delay term in the weakly nonlinear internal feedback: |ut|lutt + ∆2u - ∆utt - ∫0t h(t - s)∆2u(s) ds + μ1g1 (ut(x, t)) + μ2g2 (ut(x, t - τ)) = 0 We prove the existence of global solutions in suitable Sobolev spaces by using the energy method combined with Faedo-Galarkin method under condition on the weight of the delay term in the feedback and the weight of the term without delay. Furthermore, we study general stability estimates by using some properties of convex functions.

Description

Keywords

Global solution, Delay term, General decay, Multiplier method, Weak frictional damping, Convexity, Viscoelastic Petrovsky equation

Citation

Mezouar, N., Abdelli, M., & Rachah, A. (2017). Existence of global solutions and decay estimates for a viscoelastic Petrovsky equation with a delay term in the non-linear internal feedback. <i>Electronic Journal of Differential Equations, 2017</i>(58), pp. 1-25.

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Attribution 4.0 International

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