New general decay result for a fourth-order Moore-Gibson-Thompson equation with memory

Wenjun Liu; Zhijing Chen; Zhiyu Tu; Wenjun Liu; Zhijing Chen; Zhiyu Tu

doi:10.3934/era.2020025

Electronic Research Archive

2020, Volume 28, Issue 1: 433-457. doi: 10.3934/era.2020025

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New general decay result for a fourth-order Moore-Gibson-Thompson equation with memory

School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China

Received: 01 December 2019
Primary: 35B35, 35Q70, 35G05; Secondary: 45D05, 74D99

In this paper, we consider the fourth-order Moore-Gibson- Thompson equation with memory recently introduced by (Milan J. Math. 2017, 85: 215-234) that proposed the fourth-order model. We discuss the well-posedness of the solution by using Faedo-Galerkin method. On the other hand, for a class of relaxation functions satisfying $ g'(t)\leq-\xi(t)M(g(t)) $ for $ M $ to be increasing and convex function near the origin and $ \xi(t) $ to be a nonincreasing function, we establish the explicit and general energy decay result, from which we can improve the earlier related results.
- Well-posedness,
- general decay,
- Moore-Gibson-Thompson equation,
- energy method
Citation: Wenjun Liu, Zhijing Chen, Zhiyu Tu. New general decay result for a fourth-order Moore-Gibson-Thompson equation with memory[J]. Electronic Research Archive, 2020, 28(1): 433-457. doi: 10.3934/era.2020025

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Abstract

In this paper, we consider the fourth-order Moore-Gibson- Thompson equation with memory recently introduced by (Milan J. Math. 2017, 85: 215-234) that proposed the fourth-order model. We discuss the well-posedness of the solution by using Faedo-Galerkin method. On the other hand, for a class of relaxation functions satisfying $ g'(t)\leq-\xi(t)M(g(t)) $ for $ M $ to be increasing and convex function near the origin and $ \xi(t) $ to be a nonincreasing function, we establish the explicit and general energy decay result, from which we can improve the earlier related results.

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