一类具有临界指数非线性的波动方程的高能爆破

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2025-03-03 DOI:10.1002/mma.10873

Tahir Boudjeriou, Ngo Tran Vu, Nguyen Van Thin

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引用次数: 0

摘要

本文的目的是研究一类包含分数阶1 / 2 $$ 1/2 $$ -拉普拉斯算子的具有临界指数增长的波动方程的弱解的有限时间爆破，其中初始能量为超临界。这些结果推广了最近关于弱解有限时间爆破的工作。我们强调没有有效的方法来研究这个问题。因此，我们需要找到一些合适的假设和适当的技术来实现这一点。

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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High Energy Blowup for a Class of Wave Equations With Critical Exponential Nonlinearity

The goal of this paper is to investigate the finite-time blow-up of weak solutions to a class of wave equations involving the fractional $1 / 2$ -Laplace operator with critical exponential growth, where the initial energy is supercritical. These results extend the recent work regarding the finite-time blow-up of weak solutions. We emphasize that there are no effective methods to study this problem. Hence, we need to find some suitable assumptions and the appropriate technique to achieve this.

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来源期刊

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.