canal surface, Gauss map, Laplace operator, pseudo hyperbolic sphere, Minkowski 3-space
In this paper, we mainly investigate long-time behavior for viscoelastic equation with fading memory $ u_{tt}-\Delta u_{tt}-\nu \Delta u+\int_{0}^{+\infty}k'(s)\Delta u(t-s)ds+f(u) = g(x). $ The main feature of the above equation is that the equation doesn't contain $ -\Delta u_t...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2021-06-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2021552?viewType=HTML |
| Summary: | In this paper, we mainly investigate long-time behavior for viscoelastic equation with fading memory
$ u_{tt}-\Delta u_{tt}-\nu \Delta u+\int_{0}^{+\infty}k'(s)\Delta u(t-s)ds+f(u) = g(x). $
The main feature of the above equation is that the equation doesn't contain $ -\Delta u_t $, which contributes to a strong damping. The existence of global attractors is obtained by proving asymptotic compactness of the semigroup generated by the solutions for the viscoelastic equation. In addition, the upper semicontinuity of global attractors also is obtained.
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| ISSN: | 2473-6988 |