@article{ae3a2f1aaf644a10bc0aa4c02a0aceb1,
title = "Supercritical semilinear wave equation with non-negative potential",
abstract = "We prove a weighted L∞ estimate for the solution to the linear wave equation with a smooth positive time independent potential. The proof is based on application of generalized Fourier transform for the perturbed Laplace operator and a finite dependence domain argument. We apply this estimate to prove the existence of global small data solution to supercritical semilinear wave equations with potential.",
author = "Vladimir Georgiev and Charlotte Heiming and Hideo Kubo",
note = "Funding Information: We would like to thank Prof. Piero D{\textquoteright}Ancona for valuable remarks. The first author (Vladimir Georgiev) was partially supported by Programma Nazionale M.U.R.S.T. {\textquoteleft}{\textquoteleft}Problemi e Metodi nella Teoria delle Equazioni Iperboliche.{\textquoteright}{\textquoteright} The second author (Charlotte Heiming) was partially supported by Contract TMR-Network {\textquoteleft}{\textquoteleft}Hyperbolic Systems of Conservation Laws.{\textquoteright}{\textquoteright} The third author (Hideo Kubo) was partially supported by Grant-in-Aid for Science Research (No.09304012 and No.12740105), Ministry of Education, Science and Culture, Japan.",
year = "2001",
doi = "10.1081/pde-100107822",
language = "English",
volume = "26",
pages = "2267--2303",
journal = "Communications in Partial Differential Equations",
issn = "0360-5302",
publisher = "Taylor and Francis Ltd.",
number = "11-12",
}