Estimates for the nonlinear viscoelastic damped wave equation on compact Lie groups
| Autor: | Bhardwaj, Arun Kumar, Vishvesh Kumar, Mondal, Shyam Swarup |
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| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Proceedings of the Royal Society of Edinburgh: Section A Mathematics |
| ISSN: | 0308-2105 1473-7124 |
| Popis: | Let $G$ be a compact Lie group. In this article, we investigate the Cauchy problem for a nonlinear wave equation with the viscoelastic damping on $G$. More preciously, we investigate some $L^2$-estimates for the solution to the homogeneous nonlinear viscoelastic damped wave equation on $G$ utilizing the group Fourier transform on $G$. We also prove that there is no improvement of any decay rate for the norm $\|u(t,\cdot)\|_{L^2(G)}$ by further assuming the $L^1(G)$-regularity of initial data. Finally, using the noncommutative Fourier analysis on compact Lie groups, we prove a local in time existence result in the energy space $\mathcal{C}^1([0,T],H^1_{\mathcal L}(G)).$ 16 pages. arXiv admin note: text overlap with arXiv:2207.04422 |
| Databáze: | OpenAIRE |
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