Article ID Journal Published Year Pages File Type
5024346 Nonlinear Analysis: Real World Applications 2018 41 Pages PDF
Abstract
In this paper we consider the Cauchy problem for semi-linear de Sitter models with power non-linearity. The model of interest is ϕtt−e−2tΔϕ+nϕt+m2ϕ=|ϕ|p,(ϕ(0,x),ϕt(0,x))=(f(x),g(x)),where m2 is a non-negative constant. We study the global (in time) existence of small data solutions. In particular, we show the interplay between the power p, admissible data spaces and admissible spaces of solutions (in weak sense, in sense of energy solutions or in classical sense).
Related Topics
Physical Sciences and Engineering Engineering Engineering (General)
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