@article{d4bc58026ce14301aa43a6f22cc60eee,

title = "The lifespan of solutions of semilinear wave equations with the scale-invariant damping in one space dimension",

abstract = "The critical constant µ (see (1.1)) of time-decaying damping in the scale-invariant case is recently conjectured. It also has been expected that the lifespan estimate is the same as for the associated semilinear heat equations if the constant is in the “heat-like” domain. In this paper, we point out that this is not true if the total integral of the sum of initial position and speed vanishes. In such a case, we have a new type of the lifespan estimates which is closely related to the non-damped case in shifted space dimensions.",

author = "Masakazu Kato and Hiroyuki Takamura and Kyouhei Wakasa",

note = "Funding Information: Muroran Institute of Technology. The second author has been partially supported by Special Research Expenses in FY2017, General Topics (No.B21), Future University Hakodate, also by the Grant-in-Aid for Scientific Research (B)(No.18H01132) and (C)(No.15K04964), Japan Society for the Promotion of Science. Funding Information: This work started when the second author was working in Future University Hakodate and the third author was working in Muroran Institute of Technology. The second author has been partially supported by Special Research Expenses in FY2017, General Topics (No.B21), Future University Hakodate, also by the Grant-in-Aid for Scientific Research (B)(No.18H01132) and (C)(No.15K04964), Japan Society for the Promotion of Science. Publisher Copyright: {\textcopyright} 2019 Khayyam Publishing. All rights reserved.",

year = "2019",

language = "English",

volume = "32",

pages = "659--678",

journal = "Differential and Integral Equations",

issn = "0893-4983",

publisher = "Khayyam Publishing, Inc.",

number = "11-12",

}