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- W4287178265 abstract "In this paper we consider a semiclassical version of the wave equations with singular H{o}lder time-dependent propagation speeds on the lattice $hbarmathbb{Z}^{n}$. We allow the propagation speed to vanish leading to the weakly hyperbolic nature of the equations. Curiously, very much contrary to the Euclidean case considered by Colombini, de Giorgi and Spagnolo [2] and by other authors, the Cauchy problem, in this case, is well-posed in $ell^2(hbarmathbb{Z}^{n})$. However, we also recover the well-posedness results in the intersection of certain Gevrey and Sobolev spaces in the limit of the semiclassical parameter $hbarto 0$." @default.
- W4287178265 created "2022-07-25" @default.
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- W4287178265 date "2021-05-22" @default.
- W4287178265 modified "2023-10-01" @default.
- W4287178265 title "Discrete time-dependent wave equations I. Semiclassical analysis" @default.
- W4287178265 doi "https://doi.org/10.48550/arxiv.2105.10691" @default.
- W4287178265 hasPublicationYear "2021" @default.
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