p-Kirchhoff 型四阶双曲方程全局解的临界指数

IF 2 3区数学 Q1 MATHEMATICS, APPLIED Mathematical Methods in the Applied Sciences Pub Date : 2024-08-23 DOI:10.1002/mma.10438

Bingchen Liu, Jiaxin Dou

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引用次数: 0

摘要

我们研究了一个涉及基尔霍夫型-拉普拉奇和超线性源的四阶双曲方程，该方程受零纳维尔边界条件的限制，其中是一个开放的有界域，表示最大存在时间；和是常数。对于，我们利用辅助函数法和 Sobolev 不等式证明只有全局解。对于，我们得到了初始能量和内哈里能量的最优分类，从而保证了炸解及全局解的存在。在临界情况下，我们发现基尔霍夫项系数和超线性源对分离出弱解的性质起着重要作用。

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Critical exponent for global solutions in a fourth-order hyperbolic equation of p-Kirchhoff type

We study a fourth-order hyperbolic equation involving Kirchhoff type $p$ -Laplacian and superlinear source, subject to zero Navier boundary condition,

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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.