一类同质非线性抛物线系统解的存在性和渐近行为

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-09-17 DOI:10.1016/j.nonrwa.2024.104220

Jun Wang, Xuan Wang

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引用次数: 0

摘要

本文研究了一类有界域和无界域的同质非线性抛物线系统解的全局存在性和渐近稳定性。首先，我们利用势阱法证明了不同初始条件下系统解的全局存在性和有限时间炸毁，并考虑了解的渐近行为。另一方面，我们还得到了 Sobolev 次临界和临界情况下解的全局存在性和有限时间炸毁。我们采用比较最小能级与半微分解的方法来克服这里的困难。

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Existence and asymptotical behavior of solutions of a class of parabolic systems with homogeneous nonlinearity

In this paper we investigate the global existence and asymptotical stability of solutions to a class of parabolic systems with homogeneous nonlinearity for both bounded and unbounded domains. First we prove both global existence and finite time blow-up of solutions of the system for different initial conditions by using the potential well method, and the asymptotic behavior of the solutions are also considered. On the other hand, we also obtain global existence and finite time blow-up of solutions for both Sobolev subcritical and critical cases. We use a method of comparing least energy levels with that of semitrivial solutions to overcome the difficulties here.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.