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| Titre: | Asymptotics for a wave equation with critical exponential nonlinearity |
| Auteur(s): | Boudjeriou, Tahir
Van Thin, Nguyen |
| Mots-clés: | Asymptotic behavior
Fractional Laplacian
Stable and unstable sets
Wave equations |
| Date de publication: | 2024 |
| Editeur: | Elsevier Ltd |
| Collection/Numéro: | Nonlinear Analysis: Real World Applications/ Vol. 78, Art.N° 104099(2024);PP. 1-23 |
| Résumé: | In this paper, we discuss some qualitative analysis of solutions to the following Cauchy problem of wave equations involving the 1/2-Laplace operator with critical exponential nonlinearity [Formula presented] where λ>0, δ≥0, q>2, and α0>0. By using the contraction mapping principle, we show that the above Cauchy problem has a unique local solution. With the help of the potential well argument, we characterize the stable sets by the asymptotic behavior of solutions as t goes to infinity, as well as the unstable sets by the blow-up of solutions in finite time. |
| URI/URL: | https://doi.org/10.1016/j.nonrwa.2024.10409
https://www.sciencedirect.com/science/article/abs/pii/S1468121824000397
http://dlibrary.univ-boumerdes.dz:8080/handle/123456789/14557 |
| ISSN: | 1468-1218 |
| Collection(s) : | Publications Internationales
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