A class of fourth-order hyperbolic equations with strongly damped and nonlinear logarithmic terms

Yi Cheng; Ying Chu; Yi Cheng; Ying Chu

doi:10.3934/era.2021066

Electronic Research Archive

2021, Volume 29, Issue 6: 3867-3887. doi: 10.3934/era.2021066

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A class of fourth-order hyperbolic equations with strongly damped and nonlinear logarithmic terms

Yi Cheng ,
Ying Chu

School of Science, Changchun University of Science and Technology, Changchun 130022, China

Received: 01 June 2021 Revised: 01 July 2021 Published: 07 September 2021
Primary: 35A01, 35L75; Secondary: 35B40, 35B44

In this paper, we study a class of hyperbolic equations of the fourth order with strong damping and logarithmic source terms. Firstly, we prove the local existence of the weak solution by using the contraction mapping principle. Secondly, in the potential well framework, the global existence of weak solutions and the energy decay estimate are obtained. Finally, we give the blow up result of the solution at a finite time under the subcritical initial energy.
- Fourth-order hyperbolic equations,
- strong damping,
- global existence,
- energy decay estimate,
- blow up
Citation: Yi Cheng, Ying Chu. A class of fourth-order hyperbolic equations with strongly damped and nonlinear logarithmic terms[J]. Electronic Research Archive, 2021, 29(6): 3867-3887. doi: 10.3934/era.2021066

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Abstract

In this paper, we study a class of hyperbolic equations of the fourth order with strong damping and logarithmic source terms. Firstly, we prove the local existence of the weak solution by using the contraction mapping principle. Secondly, in the potential well framework, the global existence of weak solutions and the energy decay estimate are obtained. Finally, we give the blow up result of the solution at a finite time under the subcritical initial energy.

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