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Classification of decay estimate in a 4th-order quasilinear hyperbolic equation with strong damping

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This paper demonstrates global solutions and decay estimates in a quasilinear hyperbolic equation, highlighting implications for blow-up time.

Global solutions exist in the positive initial energy case, showing five categories of decay estimates for different exponent regions.
For negative initial energy, the study establishes bounds for blow-up time, providing critical insights into solution behavior.
The study specifies the role of the L^{2} inner product and its non-necessity for blow-up solutions in certain exponent regions.
Damping effects significantly influence solutions, suggesting that strong damping plays a critical role in the equation's behavior.

Dou et al. (2025) studied this question.

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This paper demonstrates global solutions and decay estimates in a quasilinear hyperbolic equation, highlighting implications for blow-up time.