A note to semilinear de Sitter models in 1d with balanced mass and dissipation. (June 2023) - Ebert, M.R.; Reissig, M.
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 .