On the Cauchy problem for a class of semilinear second order evolution equations with fractional Laplacian and damping

被引：6

作者：

Fujiwara, Kazumasa ^{[1
]}

Ikeda, Masahiro ^{[2
,3
]}

Wakasugi, Yuta ^{[4
]}

机构：

[1] Nagoya Univ, Grad Sch Math, Chikusa Ku, Nagoya, Aichi 4648602, Japan

[2] Keio Univ, Dept Math, Fac Sci & Technol, Kohoku Ku, 3-14-1 Hiyoshi, Yokohama, Kanagawa 2238522, Japan

[3] RIKEN, Ctr Adv Intelligence Project, Chuo Ku, 1-4-1 Nihonbashi, Tokyo 1030027, Japan

[4] Hiroshima Univ, Grad Sch Adv Sci & Engn, Lab Math, Higashihiroshima 7398527, Japan

来源：

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS | 2021年 / 28卷 / 06期

基金：

日本学术振兴会;

关键词：

Fractional Laplacian; Dissipative term; Second order evolution equation; Power nonlinearity; Asymptotic behavior; Global existence; DAMPED WAVE-EQUATION; TIME-DEPENDENT DISSIPATION; L-P; GLOBAL EXISTENCE; ASYMPTOTIC-BEHAVIOR; CRITICAL EXPONENT;

D O I：

10.1007/s00030-021-00723-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the present paper, we prove time decay estimates of solutions in weighted Sobolev spaces to the second order evolution equation with fractional Laplacian and damping for data in Besov spaces. Our estimates generalize the estimates obtained in the previous studies (Karch in Stud Math 143:175-197, 2000; Ikeda et al. in Nonlinear Differ. Equ. Appl. 24:10, 2017). The second aim of this article is to apply these estimates to prove small data global well-posedness for the Cauchy problem of the equation with power nonlinearities. Especially, the estimates obtained in this paper enable us to treat more general conditions on the nonlinearities and the spatial dimension than the results in the papers (Chen et al. in Electron. J. Differ. Equ. 2015:1-14, 2015; Ikeda et al. in Nonlinear Differ. Equ. Appl. 24:10, 2017).

引用

页数：40

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