Lifespan of solutions to a damped plate equation with logarithmic nonlinearity

Yuzhu Han; Qi Li

doi:10.3934/eect.2020101

Article Contents

2022, Volume 11, Issue 1: 25-40. Doi: 10.3934/eect.2020101

This issue Previous Article Existence and uniqueness of mild solutions for quasi-linear fractional integro-differential equations Next Article Non-autonomous 2D Newton-Boussinesq equation with oscillating external forces and its uniform attractor

Lifespan of solutions to a damped plate equation with logarithmic nonlinearity

Yuzhu Han^, and
Qi Li

School of Mathematics, Jilin University, Changchun, 130012, China

^* Corresponding author: Yuzhu Han
^* Corresponding author: Yuzhu Han

Received: April 30, 2020

Revised: July 31, 2020

Early access: October 2020

Published: February 2022

Supported by NSFC (11401252) and by Scientific Research Project of The Education Department of Jilin Province (JJKH20190018KJ)

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Abstract

This paper is devoted to the lifespan of solutions to a damped plate equation with logarithmic nonlinearity

$ u_{tt}+\Delta^2u-\Delta u-\Delta u_t+u_t = |u|^{p-2}u\ln|u|. $

Finite time blow-up criteria for solutions at both lower and high initial energy levels are established and an upper bound for the blow-up time is given for each case. Moreover, by constructing a new auxiliary functional and making full use of the strong damping term, a lower bound for the blow-up time is also derived.

Keywords:

Mathematics Subject Classification: Primary: 35L35; Secondary: 35L76.

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