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

被引：0
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作者：
Kazumasa Fujiwara
Masahiro Ikeda
Yuta Wakasugi
机构：
[1] Nagoya University,Graduate School of Mathematics
[2] Keio University,Department of Mathematics, Faculty of Science and Technology, Japan
[3] Center for Advanced Intelligence Project,Laboratory of Mathematics, Graduate School of Advanced Science and Engineering
[4] Hiroshima University,undefined
来源：
Nonlinear Differential Equations and Applications NoDEA | 2021年 / 28卷
关键词：
Fractional Laplacian; Dissipative term; Second order evolution equation; Power nonlinearity; Asymptotic behavior; Global existence; Primary 35L71; Seconary 35A01;
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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).
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