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Mathematics > Analysis of PDEs

arXiv:2209.10154 (math)
[Submitted on 21 Sep 2022 (v1), last revised 5 Oct 2022 (this version, v2)]

Title:Asymptotic profile of L^2-norm of solutions for wave equations with critical log-damping

Authors:Ruy Coimbra Charão, Ryo Ikehata
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Abstract:We consider wave equations with a special type of log-fractional damping. We study the Cauchy problem for this model in the whole space, and we obtain an asymptotic profile and optimal estimates of solutions as time goes to infinity in L^2-sense. A maximal discovery of this note is that under the effective damping, in case of n = 1 L^2-norm of the solution blows up in infinite time, and in case of n = 2 L^2-norm of the solution never decays and never blows up in infinite time. The latter phenomenon seems to be a rare case.
Comments: 24 pages, Statements of Theorems 1.3 and 1.4 and their proofs in the former version (v1) have been just corrected
Subjects: Analysis of PDEs (math.AP)
MSC classes: 35L05, 35B40, 35C20, 35S05
Cite as: arXiv:2209.10154 [math.AP]
  (or arXiv:2209.10154v2 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.2209.10154

Submission history

From: Ryo Ikehata [view email]
[v1] Wed, 21 Sep 2022 07:23:08 UTC (17 KB)
[v2] Wed, 5 Oct 2022 02:34:44 UTC (19 KB)
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