Lifespan of solutions to semilinear damping wave equations in de Sitter spacetime. (June 2020)

• Record Type: Journal Article
• Authors: Li, Hengyan; Li, Xintao; Yan, Weiping
• Is Part Of: Nonlinear analysis. Volume 195(2020)
• Publication Date: 2020-06
• Subjects: 35L05 -- 74H35; Blowup -- Wave equation -- Lifespan; 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.2019.111735
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: This paper studies blowup phenomena for two kind of initial value problem of semilinear damping wave equations in de Sitter spacetime. The first problem comes from the latter problem of conjecture of Strauss in de Sitter Spacetime, and the second problem arises from the latter problem of conjecture of Glassey in de Sitter Spacetime. We give blowup and lifespan of solutions on those two problems. Comparing with non-damping case established in Yan (2018), one can see that the damping term with a positive bounded time-dependent coefficient does not effect blowup of solutions. Meanwhile, we establish a new ODE blowup result concerning damping term.