A note to semilinear de Sitter models in 1d with balanced mass and dissipation. (June 2023)

• Record Type: Journal Article
• Authors: Ebert, M.R.; Reissig, M.
• Is Part Of: Nonlinear analysis. Volume 71(2023)
• Publication Date: 2023-06
• Subjects: 35L15 -- 35L71; Cauchy problem -- de Sitter model -- Power-nonlinearity -- Global existence -- Small data -- Fractional Gagliardo–Nirenberg inequality; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2023.103835
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper we consider the Cauchy problem for semilinear de Sitter models in 1d with balanced mass and dissipation. The model of interest is ϕ t t − e − 2 t ϕ x x + ϕ t + 1 4 ϕ = | ϕ | p, ( ϕ ( 0, x ), ϕ t ( 0, x ) ) = ( 0, g ( x ) ) . We study the global (in time) existence of small data solutions. In particular, we show by applying Schauder's fixed point theorem that there exists a Sobolev solution for all p > 1 .