TY - JOUR
T1 - On a semilinear wave equation in anti-de Sitter spacetime
T2 - The critical case
AU - Palmieri, Alessandro
AU - Takamura, Hiroyuki
N1 - Funding Information:
A. Palmieri was supported by the Japan Society for the Promotion of Science (JSPS)—JSPS Postdoctoral Fellowship for Research in Japan (Short-term) (Grant No. PE20003)—and is the member of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Instituto Nazionale di Alta Matematica (INdAM). H. Takamura was partially supported by the Grants-in-Aid for Scientific Research (A) (Grant No. 22H00097) and (B) (Grant No. 18H01132), Japan Society for the Promotion of Science. The first version of this work was prepared while A. Palmieri stayed at Mathematical Institute, Tohoku University, from July 2021 to January 2022 and while H. Takamura was the member of the Research Alliance Center of Mathematical Sciences, Tohoku University. Both authors thank the anonymous referee for his/her suggestions that helped to improve the final version of the paper.
Publisher Copyright:
© 2022 Author(s).
PY - 2022/11/1
Y1 - 2022/11/1
N2 - In the present paper, we prove the blow-up in finite time for local solutions of a semilinear Cauchy problem associated with a wave equation in anti-de Sitter spacetime in the critical case. According to this purpose, we combine a result for ordinary differential inequalities with an iteration argument by using an explicit integral representation formula for the solution to a linear Cauchy problem associated with the wave equation in anti-de Sitter spacetime in one space dimension.
AB - In the present paper, we prove the blow-up in finite time for local solutions of a semilinear Cauchy problem associated with a wave equation in anti-de Sitter spacetime in the critical case. According to this purpose, we combine a result for ordinary differential inequalities with an iteration argument by using an explicit integral representation formula for the solution to a linear Cauchy problem associated with the wave equation in anti-de Sitter spacetime in one space dimension.
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U2 - 10.1063/5.0086614
DO - 10.1063/5.0086614
M3 - Article
AN - SCOPUS:85143366017
SN - 0022-2488
VL - 63
JO - Journal of Mathematical Physics
JF - Journal of Mathematical Physics
IS - 11
M1 - 111505
ER -