紧致李群上的非线性分数阻尼波动方程

IF 1.1 4区 数学 Q2 MATHEMATICS, APPLIED Asymptotic Analysis Pub Date : 2022-11-11 DOI:10.3233/asy-231842
Aparajita Dasgupta, Vishvesh Kumar, Shyam Swarup Mondal
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引用次数: 0

摘要

本文研究了G上具有幂型非线性的紧李群上的初值分数阶阻尼波动方程。这个手稿的目的是双重的。首先,利用紧李群的傅里叶分析,证明了g上分数阶阻尼波动方程在能量空间上的局部时间存在性,并在一定条件下建立了初始数据的有限时间爆破结果。在本文的下一部分,我们考虑紧李群上具有相同幂型非线性的低阶项即阻尼和质量的分数阶波动方程,并证明了小数据解在能量演化空间中的全局实时存在性。
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Nonlinear fractional damped wave equation on compact Lie groups
In this paper, we deal with the initial value fractional damped wave equation on G, a compact Lie group, with power-type nonlinearity. The aim of this manuscript is twofold. First, using the Fourier analysis on compact Lie groups, we prove a local in-time existence result in the energy space for the fractional damped wave equation on G. Moreover, a finite time blow-up result is established under certain conditions on the initial data. In the next part of the paper, we consider fractional wave equation with lower order terms, i.e., damping and mass with the same power type nonlinearity on compact Lie groups, and prove the global in-time existence of small data solutions in the energy evolution space.
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来源期刊
Asymptotic Analysis
Asymptotic Analysis 数学-应用数学
CiteScore
1.90
自引率
7.10%
发文量
91
审稿时长
6 months
期刊介绍: The journal Asymptotic Analysis fulfills a twofold function. It aims at publishing original mathematical results in the asymptotic theory of problems affected by the presence of small or large parameters on the one hand, and at giving specific indications of their possible applications to different fields of natural sciences on the other hand. Asymptotic Analysis thus provides mathematicians with a concentrated source of newly acquired information which they may need in the analysis of asymptotic problems.
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