TY - JOUR
T1 - The lifespan of solutions of semilinear wave equations with the scale-invariant damping in two space dimensions
AU - Imai, Takuto
AU - Kato, Masakazu
AU - Takamura, Hiroyuki
AU - Wakasa, Kyouhei
N1 - Funding Information:
This work started when the first author was a master course student in Future University Hakodate, the third author was working in Future University Hakodate, and the fourth author was working in Muroran Institute of Technology. The third 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 . Finally all the authors are grateful to the referee for precise reading and useful comments.
Publisher Copyright:
© 2020 The Author(s)
PY - 2020/11/5
Y1 - 2020/11/5
N2 - In this paper, we study the initial value problem for semilinear wave equations with the time-dependent and scale-invariant damping in two dimensions. Similarly to the one dimensional case by Kato, Takamura and Wakasa in 2019, we obtain the lifespan estimates of the solution for a special constant in the damping term, which are classified by total integral of the sum of the initial position and speed. The key fact is that, only in two space dimensions, such a special constant in the damping term is a threshold between “wave-like” domain and “heat-like” domain. As a result, we obtain a new type of estimate especially for the critical exponent.
AB - In this paper, we study the initial value problem for semilinear wave equations with the time-dependent and scale-invariant damping in two dimensions. Similarly to the one dimensional case by Kato, Takamura and Wakasa in 2019, we obtain the lifespan estimates of the solution for a special constant in the damping term, which are classified by total integral of the sum of the initial position and speed. The key fact is that, only in two space dimensions, such a special constant in the damping term is a threshold between “wave-like” domain and “heat-like” domain. As a result, we obtain a new type of estimate especially for the critical exponent.
KW - Lifespan
KW - Scale-invariant damping
KW - Semilinear wave equation
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U2 - 10.1016/j.jde.2020.06.019
DO - 10.1016/j.jde.2020.06.019
M3 - Article
AN - SCOPUS:85086457605
SN - 0022-0396
VL - 269
SP - 8387
EP - 8424
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 10
ER -