Global existence and blow-up for semilinear damped wave equations in three space dimensions. (May 2019)

• Record Type: Journal Article
• Authors: Kato, Masakazu; Sakuraba, Miku
• Is Part Of: Nonlinear analysis. Volume 182(2019)
• Page Start: 209
• Page End: 225
• Publication Date: 2019-05
• Subjects: 35L71 -- 35E15 -- 35A01; Semilinear damped wave equation -- Blow-up -- Lifespan -- Three space dimensions; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2018.12.013
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We consider initial value problem for semilinear damped wave equations in three space dimensions. We show the small data global existence for the problem without the spherically symmetric assumption and obtain the sharp lifespan of the solutions. This paper is devoted to a proof of the Takamura's conjecture in D'Abbicco et al. (2015) on the lifespan of solutions.