@article{e43a02ae78c1467abd2e965386d35e3b,
title = "Critical exponent for nonlinear damped wave equations with non-negative potential in 3D",
abstract = "We are studying possible interaction of damping coefficients in the subprincipal part of the linear 3D wave equation and their impact on the critical exponent of the corresponding nonlinear Cauchy problem with small initial data. The main new phenomena is that certain relation between these coefficients may cause very strong jump of the critical Strauss exponent in 3D to the critical 5D Strauss exponent for the wave equation without damping coefficients.",
author = "Vladimir Georgiev and Hideo Kubo and Kyouhei Wakasa",
note = "Funding Information: The first author was supported in part by Project 2017 “Problemi stazionari e di evoluzione nelle equazioni di campo nonlineari” of INDAM, GNAMPA - Gruppo Nazionale per l'Analisi Matematica, la Probabilit{\`a} e le loro Applicazioni, by Institute of Mathematics and Informatics, Bulgarian Academy of Sciences and Top Global University Project, Waseda University, by the University of Pisa, Project PRA 2018 49 and project “Dinamica di equazioni nonlineari dispersive”, “Fondazione di Sardegna”, 2016.The second author was partially supported by Grant-in-Aid for Science Research (No. 16H06339 and No. 26220702), JSPS.The third author was partially supported by Grant-in-Aid for Scientific Research (No. 18H01132), JSPS. We are grateful to Professor M. Ikeda and Professor M. Sobajima for valuable discussion during the preparation of this work. We also thank the referee for the careful reading and useful suggestions. Funding Information: The first author was supported in part by Project 2017 ?Problemi stazionari e di evoluzione nelle equazioni di campo nonlineari? of INDAM, GNAMPA - Gruppo Nazionale per l'Analisi Matematica, la Probabilit? e le loro Applicazioni, by Institute of Mathematics and Informatics, Bulgarian Academy of Sciences and Top Global University Project, Waseda University, by the University of Pisa, Project PRA 2018 49 and project ?Dinamica di equazioni nonlineari dispersive?, ?Fondazione di Sardegna?, 2016.The second author was partially supported by Grant-in-Aid for Science Research (No. 16H06339 and No. 26220702), JSPS.The third author was partially supported by Grant-in-Aid for Scientific Research (No. 18H01132), JSPS. We are grateful to Professor M. Ikeda and Professor M. Sobajima for valuable discussion during the preparation of this work. We also thank the referee for the careful reading and useful suggestions. Publisher Copyright: {\textcopyright} 2019 Elsevier Inc.",
year = "2019",
month = aug,
day = "15",
doi = "10.1016/j.jde.2019.04.004",
language = "English",
volume = "267",
pages = "3271--3288",
journal = "Journal of Differential Equations",
issn = "0022-0396",
publisher = "Academic Press Inc.",
number = "5",
}