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September 10, 2025

Bounds for Blow‐Up Time and Decay Estimate of a Fourth‐Order Hyperbolic Equation With Logarithmic Nonlinearity

Key Points

Solutions of the fourth-order hyperbolic equation blow up in finite time, indicating critical time constraints.
The derived lifespan estimates show specific bounds on how long the solutions persist before blow-up occurs.
Using the method of Levine concavity combined with differential inequalities enhances understanding of blow-up behavior.
Establishing an explicit energy decay rate highlights the performance and stability of the solutions over time.

Abstract

ABSTRACT In this paper, a class of fourth‐order hyperbolic equation with logarithmic nonlinearity is considered. It is proved that the solutions blow up in finite time by developing the method of Levine concavity and using some differential inequality techniques. Meanwhile, the lifespan of the solutions is estimated. Furthermore, we establish an explicit energy decay rate.

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Authors

Shuai Zhang

Yunzhu Gao

Beihua University

Ge Zu

Electric Power University

Journals

Mathematical Methods in the Applied Sciences

Actions

Institutions

Northeast Electric Power University

Beihua University

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Bounds for Blow‐Up Time and Decay Estimate of a Fourth‐Order Hyperbolic Equation With Logarithmic Nonlinearity

Key Points

Abstract

Citation Network

Connected Papers

Discussion

Authors

Journals

Actions

Institutions

References and Citations

Citation Network

Connected Papers

Discussion

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