@article{1817a194d5ef4873bae98e3c1f6ba687,
title = "Nonexistence of global solutions of nonlinear wave equations with weak time-dependent damping related to Glassey{\textquoteright}s conjecture",
abstract = "This work is devoted to the nonexistence of global-in-time energy solutions of nonlinear wave equation of derivative type with weak time-dependent damping in the scattering and scale invariant range. By introducing some multipliers to absorb the damping term, we succeed in establishing the same upper bound of the lifespan for the scattering damping as the non-damped case, which is a part of so-called Glassey{\textquoteright}s conjecture on nonlinear wave equations. We also study an upper bound of the lifespan for the scale invariant damping with the same method.",
author = "Lai, {Ning An} and Hiroyuki Takamura",
note = "Funding Information: b(s)ds + 1 = (s + 1) ds + 1 ≈ (t + 1) . 00 Acknowledgement. The first author was partially supported by Grant-in-Aid for Young Scientists (B) 15K17571. The second author was supported in part by Grant-in-Aid for JSPS Research Fellow 17J01263. Funding Information: The first author is partially supported by Natural Science Foundation of Zhejiang Province (LY18A010008), NSFC(11501273, 11726612, 11726611, 11771194, 11771359), Chinese Postdoctoral Science Foundation (2017M6201-28), the Scientific Research Foundation of the First-Class Discipline of Zhejiang Province (B)(201601). The second author is partially supported by the Grant-in-Aid for Scientific Research (C) (No. 15K04964), Japan Society for the Promotion of Science, and Special Research Expenses in FY2017, General Topics (No. B21), Future University Hakodate. The authors would like to express their sincere thanks to the reviewers, for their helpful suggestion to modify the paper. Publisher Copyright: {\textcopyright} 2019 Khayyam Publishing. All rights reserved.",
year = "2019",
month = feb,
language = "English",
volume = "32",
pages = "37--48",
journal = "Differential and Integral Equations",
issn = "0893-4983",
publisher = "Khayyam Publishing, Inc.",
number = "1-2",
}