info:eu-repo/semantics/article
Blow-up results for a viscoelastic beam equation of p-Laplacian type with strong damping and logarithmic source
Fecha
2023Registro en:
01704214
Mathematical Methods in the Applied Sciences
0000000121541816
Autor
Carvalho Pereira, Ducival
Araújo, Geraldo M.
Raposo, Carlos A.
Cabanillas Zannini, Victor Rafael
Institución
Resumen
In this paper, we investigate the existence, uniqueness, exponential decay, and blow-up behavior of the viscoelastic beam equation involving the (Formula presented.) -Laplacian operator, strong damping, and a logarithmic source term, given by (Formula presented.) where (Formula presented.) is a bounded domain of (Formula presented.) and (Formula presented.) is a memory kernel. Using the Faedo–Galerkin approximation, we establish the existence and uniqueness result for the global solutions, taking into account that the initial data must belong to an appropriate stability set created from the Nehari manifold. The study of the exponential decay of our problem is based on Nakao's method. Finally, the blow-up behavior on the instability set is proved.