具有可变指数和奇异势能的伪抛物方程中的初能量分类

IF 0.7 4区数学 Q2 MATHEMATICS

Bulletin of The Iranian Mathematical Society Pub Date : 2024-01-29 DOI:10.1007/s41980-023-00844-x

Xizheng Sun, Zhiqing Han, Bingchen Liu

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引用次数: 0

摘要

本文涉及一个具有奇异势和可变指数的伪抛物方程。首先，我们确定了变指数 Sobolev 空间中弱解的存在性和唯一性。其次，在变分法的框架下，我们完全利用初始能量对解的吹胀和全局存在性进行了分类。第三，我们得到了所有可能的初始能量的炸开时间下限和上限。本文的结果与恒定指数的相应问题是兼容的。本文的部分结果扩展了Lian等（J Differ Equ 269:4914-4959, 2020）、Xu和Su（J Funct Anal 264:2732-2763, 2013）以及Liu和Yu（J Funct Anal 274:1276-1283, 2018）的最新结果。

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Classification of Initial Energy in a Pseudo-parabolic Equation with Variable Exponents and Singular Potential

This paper deals with a pseudo-parabolic equation with singular potential and variable exponents. First, we determine the existence and uniqueness of weak solutions in Sobolev spaces with variable exponents. Second, in the frame of variational methods, we classify the blow-up and the global existence of solutions completely using the initial energy. Third, we obtain lower and upper bounds of blow-up time for all possible initial energy. The results in this paper are compatible with the corresponding problems with constant exponents. Part results of the paper extend the recent ones in Lian et al. (J Differ Equ 269:4914–4959, 2020), Xu and Su (J Funct Anal 264:2732–2763, 2013), and Liu and Yu (J Funct Anal 274:1276–1283, 2018).

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来源期刊

Bulletin of The Iranian Mathematical Society Mathematics-General Mathematics

CiteScore

1.40

自引率

0.00%

发文量

期刊介绍： The Bulletin of the Iranian Mathematical Society (BIMS) publishes original research papers as well as survey articles on a variety of hot topics from distinguished mathematicians. Research papers presented comprise of innovative contributions while expository survey articles feature important results that appeal to a broad audience. Articles are expected to address active research topics and are required to cite existing (including recent) relevant literature appropriately. Papers are critically reviewed on the basis of quality in its exposition, brevity, potential applications, motivation, value and originality of the results. The BIMS takes a high standard policy against any type plagiarism. The editorial board is devoted to solicit expert referees for a fast and unbiased review process.