Electron. J. Differential Equations, Vol. 2025 (2025), No. 39, pp. 1-14.
Blow-up solutions for damped Rao-Nakra beams with source terms
Mirelson M. Freitas, Mauro L. Santos, Carlos A. Raposo, Anderson A. Ramos, Jorge Ferreira
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.
DOI: 10.58997/ejde.2025.39
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Mirelson M. Freitas
Department of Mathematics
University of Brasília
Brasília 0910-900, Brazil
email: m.m.freitas@mat.unb.br
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Mauro L. Santos
Institute of Exact and Natural Sciences
Federal University of Pará
Belém - PA 66075-110, Brazil
email: ls@ufpa.br
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Carlos A. Raposo
Faculty of Mathematics
Federal University of Pará
Salinópolis - PA 68721-000, Brazil
email: carlosraposo@ufpa.br
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Anderson A. Ramos
Faculty of Mathematics
Federal University of Pará
Salinópolis - PA 68721-000, Brazil
email: ramos@ufpa.br
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Jorge Ferreira
Department of Exact Sciences
Federal Fluminense University
Volta Redonda - RJ 27255-126, Brazil
email: jorge_ferreira@id.uff.br
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