Initial boundary value problem for a strongly damped wave equation with a general nonlinearity

Hui Yang; Yuzhu Han

doi:10.3934/eect.2021019

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2022, Volume 11, Issue 3: 635-648. Doi: 10.3934/eect.2021019

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Initial boundary value problem for a strongly damped wave equation with a general nonlinearity

Hui Yang and
Yuzhu Han^,

School of Mathematics, Jilin University, Changchun 130012, China

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

Received: October 2020

Revised: February 2021

Published: June 2022

The first author is supported by NSFC grant 11401252 and by The Education Department of Jilin Province grant JJKH20190018KJ

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Abstract

In this paper, a strongly damped semilinear wave equation with a general nonlinearity is considered. With the help of a newly constructed auxiliary functional and the concavity argument, a general finite time blow-up criterion is established for this problem. Furthermore, the lifespan of the weak solution is estimated from both above and below. This partially extends some results obtained in recent literatures and sheds some light on the similar effect of power type nonlinearity and logarithmic nonlinearity on finite time blow-up of solutions to such problems.

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Mathematics Subject Classification: Primary: 35L20, 35B44; Secondary: 35L71.

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