A general stability result for a nonlinear viscoelastic equation with variable exponents
Abstract This work is concerned with a viscoelastic equation with nonlinearities of variable exponents. Firstly, the global existence of solution is obtained. Then, a general decay result of the global solution is derived via the perturbed energy method and some formulas related to convex functions....
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2025-02-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13661-025-02020-y |
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| Summary: | Abstract This work is concerned with a viscoelastic equation with nonlinearities of variable exponents. Firstly, the global existence of solution is obtained. Then, a general decay result of the global solution is derived via the perturbed energy method and some formulas related to convex functions. The kernel function under consideration belongs to a wider class of functions. More precisely, it does not need to satisfy the condition related to differential inequalities involving itself; it just needs to stay below a certain known function. The results in this work expand and generalize those in the literature regarding problems with variable exponents. |
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| ISSN: | 1687-2770 |