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Initial boundary value problem for a viscoelastic wave equation with Balakrishnan–Taylor damping and a delay term: decay estimates and blow-up result

Article scientifique 2023 Autre

Résumé

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 $g'(t)\leq -\xi (t)g^{r}(t)$ g′(t)≤−ξ(t)gr(t) , $t\geq 0$ t≥0 , $1\leq r< \frac{3}{2}$ 1≤r<32 . 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.

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Gheraibia, B., Boumaza, N. (2023). Initial boundary value problem for a viscoelastic wave equation with Balakrishnan–Taylor damping and a delay term: decay estimates and blow-up result. https://doi.org/10.1186/s13661-023-01781-8

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Auteur(s)

Billel Gheraibia Nouri Boumaza

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