Qualitative properties of solutions to the viscoelastic beam equation with damping and logarithmic nonlinear source terms

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This analysis demonstrates local existence of weak solutions in viscoelastic beams, implying conditions for blow-up and stability.

Weak solutions to the viscoelastic beam equation show local existence under specific conditions.
The study identifies sharp conditions for energy classification related to stable and unstable sets.
Derived estimates provide insights into finite-time blow-up for solutions with varying initial energy.
Application of the Faedo-Galerkin method highlights significant mathematical techniques in solving complex equations.

Gao et al. (2025) studied this question.

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