Affiliation:
1. Department of Mathematics State University of Pará Pará Brazil
2. Department of Mathematics Federal University of Pará Pará Brazil
3. Department of Mathematics Federal University of Bahia Bahia Brazil
4. Programa de Estudios Generales Universidad de Lima Lima Peru
Abstract
In this paper, we investigate the existence, uniqueness, exponential decay, and blow‐up behavior of the viscoelastic beam equation involving the
‐Laplacian operator, strong damping, and a logarithmic source term, given by
where
is a bounded domain of
and
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.
Subject
General Engineering,General Mathematics
Cited by
4 articles.
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