Global well‐posedness and finite time blow‐up for a class of wave equation involving fractional p‐Laplacian with logarithmic nonlinearity

Tahir Boudjeriou

Mathematische Nachrichten, 2023, vol. 296, issue 3, 938-956

Abstract: In this paper, we consider the following class of wave equation involving fractional p‐Laplacian with logarithmic nonlinearity utt+(−Δ)psu=|u|q−2ulog(|u|)inΩ,t>0,u=0inRN∖Ω,t>0,u(x,0)=u0(x),ut(x,0)=v0(x)inΩ,$$\begin{equation*} \hspace*{4pc}{\left\lbrace \def\eqcellsep{&}\begin{array}{llc}u_{tt}+(-\Delta )^{s}_{p}u=|u|^{q-2}u\log (|u|) & \text{in}\ & \Omega ,\;t>0 , \\[3pt] u =0 & \text{in} & \mathbb {R}^{N}\backslash \Omega ,\;t > 0, \\[3pt] u(x,0)=u_{0}(x),\,\,\,\,u_{t}(x,0)=v_{0}(x)& \text{in} &\Omega , \end{array} \right.} \end{equation*}$$where Ω⊂RN(N≥1)$\Omega \subset \mathbb {R}^N \, (N\ge 1)$ is a bounded domain with Lipschitz boundary, s∈(0,1)$s\in (0,1)$, 2≤p

Date: 2023
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