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Mathematics > Analysis of PDEs

arXiv:1804.11073 (math)
[Submitted on 30 Apr 2018 (v1), last revised 19 Nov 2018 (this version, v3)]

Title:Wave-like blow-up for semilinear wave equations with scattering damping and negative mass term

Authors:Ning-An Lai, Nico Michele Schiavone, Hiroyuki Takamura
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Abstract:In this paper we establish blow-up results and lifespan estimates for semilinear wave equations with scattering damping and negative mass term for subcritical power, which is the same as that of the corresponding problem without mass term, and also the same as that of the corresponding problem without both damping and mass term. For this purpose, we have to use the comparison argument twice, due to the damping and mass term, in additional to a key multiplier. Finally, we get the desired results by an iteration argument.
Comments: 20 pages. The last equation in Introduction of the first version has a typo. Its was trivial but revised. "mass" in the title of the second version is replaced with "mass term"
Subjects: Analysis of PDEs (math.AP)
MSC classes: primary 35L71, secondary 35B44
Cite as: arXiv:1804.11073 [math.AP]
  (or arXiv:1804.11073v3 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1804.11073
Journal reference: New tools for nonlinear PDEs and application, 217-240, Trends Math., Birkhäuser/Springer, Cham, 2019
Related DOI: https://doi.org/10.1007/978-3-030-10937-0_8

Submission history

From: Hiroyuki Takamura [view email]
[v1] Mon, 30 Apr 2018 08:11:45 UTC (14 KB)
[v2] Mon, 7 May 2018 13:05:55 UTC (14 KB)
[v3] Mon, 19 Nov 2018 09:51:24 UTC (34 KB)
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