%0 Journal Article
%T 一类具有对数非线性项的分数阶阻尼波方程的局部适定性<br>Local Well-Posedness for a Classof Fractional Damped Wave Equations with Logarithmic Nonlinearity
%A 林玲娜
%J Advances in Applied Mathematics
%P 1474-1482
%@ 2324-8009
%D 2023
%I Hans Publishing
%R 10.12677/AAM.2023.124152
%X 本文主要考虑具有对数非线性项的分数阶阻尼波动方程<img src=\"Edit_2af21b1a-78ba-48fd-badf-4c9b115f7e4c.png\" alt=\"\" />的初边值 问题，其中s ∈ (0, 1)。 算子(？？)<sup>s</sup>为分数阶Laplace算子，近年来，该算子成为了物理学、 金融数 学、  流体动力学等学科领域中的研究热点。  本文在任意初始能量下，利用Galerkin逼近法和压缩
映射原理，证明该方程解的局部适定性。<br />
In this paper, we mainly deal with the initial-boundary value problem for the frac- tional damped wave equations <img src=\"Edit_cf1790ee-8689-46b9-987b-fa48a44d02a4.png\" alt=\"\" />, where s ∈ (0, 1). The operator (？？)<sup>s</sup> is the fractional Laplace operator. In recent years, this operator has
become a research hotspot in physics, financial mathematics, fluid dynamics and oth- er disciplines. At the arbitrary initial energy levels, the local well-posedness of weak solutions to above problem is proved by using Galerkin approximation method and contraction mapping principle under some certain conditions.
%K 阻尼波动方程，分数阶Laplace算子，对数非线性项，局部适定性<br>Damped Wave Equations
%K Fractional Laplace Operator
%K Logarithmic Nonlinearity
%K Local Well-Posedness
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=64071