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

IF 1 3区数学 Q2 MATHEMATICS

Mathematische Nachrichten Pub Date : 2022-11-25 DOI:10.1002/mana.202000266

Tahir Boudjeriou

引用次数: 2

Abstract

In this paper, we consider the following class of wave equation involving fractional p-Laplacian with logarithmic nonlinearity

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一类具有对数非线性的分数阶p -拉普拉斯波动方程的全局适定性和有限时间爆破

本文考虑以下一类涉及分数阶p‐拉普拉斯方程的对数非线性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， $$\begin{equation*} \hspace*{4pc}{\left\lbrace \def\eqcellsep{&}\begin{array}{llc}u_{tt}+(-\Delta )^{s}_{p}u=|u|^{q-2}u\log (|u|) & \text{in}\ & \Omega ,\;t>0 , \\[3pt] u =0 & \text{in} & \mathbb {R}^{N}\backslash \Omega ,\;t > 0, \\[3pt] u(x,0)=u_{0}(x),\,\,\,\,u_{t}(x,0)=v_{0}(x)& \text{in} &\Omega , \end{array} \right.} \end{equation*}$$其中Ω∧RN(N≥1)$\Omega \subset \mathbb {R}^N \, (N\ge 1)$是具有Lipschitz边界的有界域，s∈(0,1)$s\in (0,1)$, 2≤p

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematische Nachrichten 数学-数学

CiteScore

1.50

自引率

0.00%

发文量

157

审稿时长

4-8 weeks

期刊介绍： Mathematische Nachrichten - Mathematical News publishes original papers on new results and methods that hold prospect for substantial progress in mathematics and its applications. All branches of analysis, algebra, number theory, geometry and topology, flow mechanics and theoretical aspects of stochastics are given special emphasis. Mathematische Nachrichten is indexed/abstracted in Current Contents/Physical, Chemical and Earth Sciences; Mathematical Review; Zentralblatt für Mathematik; Math Database on STN International, INSPEC; Science Citation Index