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- Title
Initial boundary value problem for a viscoelastic wave equation with Balakrishnan–Taylor damping and a delay term: decay estimates and blow-up result.
- Authors
Gheraibia, Billel; Boumaza, Nouri
- Abstract
In this paper, we study the initial boundary value problem for the following viscoelastic wave equation with Balakrishnan–Taylor damping and a delay term where the relaxation function satisfies g ′ (t) ≤ − ξ (t) g r (t) , t ≥ 0 , 1 ≤ r < 3 2 . The main goal of this work is to study the global existence, general decay, and blow-up result. The global existence has been obtained by potential-well theory, the decay of solutions of energy has been established by introducing suitable energy and Lyapunov functionals, and a blow-up result has been obtained with negative initial energy.
- Subjects
BOUNDARY value problems; INITIAL value problems
- Publication
Boundary Value Problems, 2023, Vol 2023, Issue 1, p1
- ISSN
1687-2762
- Publication type
Article
- DOI
10.1186/s13661-023-01781-8