Electronic Journal of Differential Equations, Vol. 2025 (2025), No. 39, pp. 1-14.

Title: Blow-up solutions for damped Rao-Nakra beams with source terms

Authors: Mirelson M. Freitas (Univ. of Brasilia, Brasilia, Brazil)
         Mauro L. Santos (Federal Univ. of Para, Belem - PA 66075-110, Brazil)
         Carlos A. Raposo (Federal Univ. of Para, Saliopolis - PA 68721-000, Brazil)
         Anderson A. Ramos (Federal Univ. of Para, Saliopolis - PA 68721-000, Brazil)
         Jorge Ferreira (Federal Fluminense Univ, Volta Redonda - RJ 27255-126, Brazil)

Abstract:
This article concerns the blow-up of solutions for a damped Rao-Nakra beam 
equation with nonlinear source terms at arbitrary initial energy levels. 
We estimate the lower and upper bounds of the lifespan of the blow-up solution 
and the blow-up rate by considering both linear and nonlinear weak damping 
terms.

Submitted November 5, 2024. Published April 10, 2025.
Math Subject Classifications: 35B40, 35B41, 37B55, 37L30.
Key Words: Rao-Nakra beam; nonlinear damping; source term; blow-up.