二维广义扎哈罗夫-库兹涅佐夫-伯格斯方程解的最优衰减估计和渐近曲线

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY
Ikki Fukuda , Hiroyuki Hirayama
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引用次数: 0

摘要

我们考虑的是二维广义扎哈罗夫-库兹涅佐夫-伯格斯方程的柯西问题。这是非线性色散-耗散方程之一,其中有一个空间各向异性耗散项 -μuxx。本文证明,只要初始数据 u0(x,y) 满足 u0∈L1(R2) 和一些适当的正则性假设,该问题的解在 L∞ 意义上以 t-34 的速率衰减。此外,我们还研究了更详细的大时间行为,并得到了解的 L∞ 值下限。因此,我们证明了给定的衰减率 t-34 是最优解。此外,结合抛物方程和薛定谔方程所用的技术,我们得出了解的显式渐近曲线。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Optimal decay estimate and asymptotic profile for solutions to the generalized Zakharov–Kuznetsov–Burgers equation in 2D

We consider the Cauchy problem for the generalized Zakharov–Kuznetsov–Burgers equation in 2D. This is one of the nonlinear dispersive–dissipative equations, which has a spatial anisotropic dissipative term μuxx. In this paper, we prove that the solution to this problem decays at the rate of t34 in the L-sense, provided that the initial data u0(x,y) satisfies u0L1(R2) and some appropriate regularity assumptions. Moreover, we investigate the more detailed large time behavior and obtain a lower bound of the L-norm of the solution. As a result, we prove that the given decay rate t34 of the solution to be optimal. Furthermore, combining the techniques used for the parabolic equations and for the Schrödinger equation, we derive the explicit asymptotic profile for the solution.

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来源期刊
Accounts of Chemical Research
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.
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