The existence, general decay and blow-up for a plate equation with nonlinear damping and a logarithmic source term

Gongwei Liu; Gongwei Liu

doi:10.3934/era.2020016

Electronic Research Archive

2020, Volume 28, Issue 1: 263-289. doi: 10.3934/era.2020016

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The existence, general decay and blow-up for a plate equation with nonlinear damping and a logarithmic source term

Gongwei Liu ^,

College of Science, Henan University of Technology, Zhengzhou 450001, China

Received: 01 November 2019
Primary: 35A01, 35G31; Secondary: 35B40, 35B44

In this paper, we consider a plate equation with nonlinear damping and logarithmic source term. By the contraction mapping principle, we establish the local existence. The global existence and decay estimate of the solution at subcritical initial energy are obtained. We also prove that the solution with negative initial energy blows up in finite time under suitable conditions. Moreover, we also give the blow-up in finite time of solution at the arbitrarily high initial energy for linear damping (i.e. $ m = 2 $).
- Plate equation,
- logarithmic source,
- decay estimate,
- blow-up
Citation: Gongwei Liu. The existence, general decay and blow-up for a plate equation with nonlinear damping and a logarithmic source term[J]. Electronic Research Archive, 2020, 28(1): 263-289. doi: 10.3934/era.2020016

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Abstract

In this paper, we consider a plate equation with nonlinear damping and logarithmic source term. By the contraction mapping principle, we establish the local existence. The global existence and decay estimate of the solution at subcritical initial energy are obtained. We also prove that the solution with negative initial energy blows up in finite time under suitable conditions. Moreover, we also give the blow-up in finite time of solution at the arbitrarily high initial energy for linear damping (i.e. $ m = 2 $).

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