Thresholds for low regularity solutions to wave equations with structural damping

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:494

Article

Fukushima, Tomonori¹  Ikehata, Ryo¹  Michihisa, Hironori² 

[1] Hiroshima Univ, Grad Sch Educ, Dept Math, Higashihiroshima 7398524, Japan

[2] Hiroshima Univ, Grad Sch Sci, Dept Math, Higashihiroshima 7398526, Japan

关键词: Structural damping;    Regularity-loss;    Low regularity;    Asymptotic profile;    Diffusion wave property;    Non-diffusive structure;    Threshold;   

DOI  :  10.1016/j.jmaa.2020.124669

来源: Elsevier

【 摘 要 】

We study the asymptotic behavior of solutions to wave equations with the structural damping term u(tt) - Delta u + Delta(2)u(t) = 0, u(0, x) = u(0)(x), u(t) (0, x) = u(1)(x), in the whole space. New thresholds are reported in this paper that indicate which of the diffusion wave property and the non-diffusive structure dominates in low regularity cases. We develop to that end the previous authors' research [2] where they have proposed a threshold that expresses whether the parabolic-like property or the wave-like property strongly appears in the solution to some regularity-loss type dissipative wave equation. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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