Optimal L2-growth of the generalized Rosenau equation

被引：0

作者：

Li, Xiaoyan ^{[1
]}

Ikehata, Ryo ^{[2
]}

机构：

[1] Hainan Univ, Sch Math & Stat, Haikou 570228, Hainan, Peoples R China

[2] Hiroshima Univ, Grad Sch Humanities & Social Sci, Dept Math, Div Educ Sci, Higashihiroshima 7398524, Japan

来源：

JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS | 2024年 / 15卷 / 03期

关键词：

Rosenau equation; Fourier analysis; Weighted L-1-data; Low dimensional case; Growth estimates; WAVE-EQUATIONS; ASYMPTOTIC PROFILES; PLATE EQUATION; CAUCHY-PROBLEM; DECAY-RATES; INEQUALITIES; EXISTENCE; DYNAMICS; BEHAVIOR;

D O I：

10.1007/s11868-024-00635-w

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We report that the quantity measured in the L-2 norm of the solution itself of the generalized Rosenau equation, which was completely unknown in this equation, grows in the proper order at time infinity. It is also immediately apparent that this growth aspect does not occur in three or more spatial dimensions, so we will apply the results obtained in this study to provide another proof that Hardy-type inequalities do not hold in the case of one or two spatial dimensions.

引用

页数：28

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