@article{fcb21b488966489eb13cd420d80470c9,
title = "Existence of solutions for a higher-order semilinear parabolic equation with singular initial data",
abstract = "We establish the existence of solutions of the Cauchy problem for a higher-order semilinear parabolic equation by introducing a new majorizing kernel. We also study necessary conditions on the initial data for the existence of local-in-time solutions and identify the strongest singularity of the initial data for the solvability of the Cauchy problem.",
keywords = "Higher-order semilinear parabolic equation, Majorizing kernel, Singular initial data, Solvability",
author = "Kazuhiro Ishige and Tatsuki Kawakami and Shinya Okabe",
note = "Funding Information: The authors would like to thank the referees for their careful readings and useful comments. The authors of this paper were supported in part by the Grant-in-Aid for Scientific Research (S) (No. 19H05599 ), from Japan Society for the Promotion of Science . The second author was also supported in part by the Grant-in-Aid for Young Scientists (B) (No. 16K17629 ) from Japan Society for the Promotion of Science . Publisher Copyright: {\textcopyright} 2020 Elsevier Masson SAS",
year = "2020",
month = sep,
day = "1",
doi = "10.1016/j.anihpc.2020.04.002",
language = "English",
volume = "37",
pages = "1185--1209",
journal = "Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis",
issn = "0294-1449",
publisher = "Elsevier Masson SAS",
number = "5",
}