Initial boundary value problem for a viscoelastic wave equation with Balakrishnan–Taylor damping and a delay term: decay estimates and blow-up result
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 ) $g'(t)\leq -\xi (t)g^{r}(t)$ , t ≥ 0 $t\geq 0$ , 1 ≤ r <...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2023-09-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13661-023-01781-8 |
| Summary: | 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 ) $g'(t)\leq -\xi (t)g^{r}(t)$ , t ≥ 0 $t\geq 0$ , 1 ≤ r < 3 2 $1\leq r< \frac{3}{2}$ . 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. |
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| ISSN: | 1687-2770 |