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

Author(s)

Ebert, M. R. ^[1] ; Reissig, M. ^[2]

Affiliation

^[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

• Document type: Journal article
• Source: NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS; v. 40, p. 14-54, APR 2018.
• Web of Science Citations: 3

Abstract

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. (AU)

• FAPESP's process: 13/20297-8 - Decay estimates for hyperbolic partial differential equations in the L^p-L^q framework
• Grantee: Marcelo Rempel Ebert
• Support Opportunities: Scholarships abroad - Research
• FAPESP's process: 15/16038-2 - Lp-Lq decay estimates for Evolution Operators
• Grantee: Marcelo Rempel Ebert
• Support Opportunities: Regular Research Grants