Dynamics of solutions to a semilinear plate equation with memory

Jinxing Liu; Xiongrui Wang; Jun Zhou; Xu Liu

doi:10.3934/cpaa.2021137

Article Contents

2021, Volume 20, Issue 11: 3911-3936. Doi: 10.3934/cpaa.2021137 open access

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Dynamics of solutions to a semilinear plate equation with memory

1.
Department of Mathematics, Yibin University, Yibin, Sichuan, 644000, China
2.
School of Mathematics and Statistics, Southwest University, Chongqing, 400715, China

^* Corresponding author
^* Corresponding author

Received: February 28, 2021

Revised: June 30, 2021

Early access: August 2021

Published: November 2021

The work of Jinxing Liu is supported by the Talent project of Yibin University (No. 2018RC17), and the work of Jun Zhou is supported by the Basic and Advanced Research Project of CQC-STC grant cstc2016jcyjA0018, NSFC 11201380

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Abstract

In this paper we consider an initial-boundary value problem of a semilinear regularity-loss-type plate equation with memory in a bounded domain of $ \mathbb{R}^n $ ($ n = 1,2,\cdots $). By using the Faedo-Galërkin method and some theories of ordinary differential equations, we obtain the local existence and uniqueness of weak solutions. Then, we study the dynamics of the weak solutions, such as global existence and finite time blow-up, by energy estimation and some ordinary differential inequalities. Moreover, the upper bound of blow-up time for the blow-up solutions is also considered.

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Mathematics Subject Classification: Primary: 35G25; Secondary: 35L30, 35B40.

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