Regularity theory and global existence of small data solutions to semi-linear de Sitter models with power non-linearity

被引：19

作者：

Ebert, M. R. ^{[1
]}

Reissig, M. ^{[2
]}

机构：

[1] Univ Sao Paulo, Dept Comp & Matemat, FFCLRP, Av Bandeirantes 3900, BR-14040901 Ribeirao Preto, SP, Brazil

[2] Tech Univ Bergakad Freiberg, Fac Math & Comp Sci, Pruferstr 9, D-09596 Freiberg, Germany

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2018年 / 40卷

基金：

巴西圣保罗研究基金会;

关键词：

de Sitter model; Power-nonlinearity; Small data global existence; Fractional chain rule; Fractional Leibniz rule; Fractional Gagliardo Nirenberg; inequality; KLEIN-GORDON EQUATIONS; SCALAR FIELD; WAVE MODELS; SPACETIME; PROPAGATION; SPEED;

D O I：

10.1016/j.nonrwa.2017.08.009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we consider the Cauchy problem for semi-linear de Sitter models with power non-linearity. The model of interest is phi tt-e(-2t)Delta phi+n phi t+m(2 phi)=vertical bar phi vertical bar, (phi(0,x),phi t(0,x))=(f(x),g(x)) where m(2) 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). (C) 2017 Elsevier Ltd. All rights reserved.

引用

页码：14 / 54

页数：41

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