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 ϕtt−e−2tϕxx+ϕt+14ϕ=|ϕ|p,(ϕ(0,x),ϕt(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.
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