### Electronic Research Archive

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

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

• 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.

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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• 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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