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

Autor(es)

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

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS; v. 40, p. 14-54, APR 2018.
• Citações Web of Science: 3

Resumo

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)

• Processo FAPESP: 13/20297-8 - Estimativas do tipo L^p-L^q para equações diferenciais parciais hiperbólicas
• Beneficiário: Marcelo Rempel Ebert
• Modalidade de apoio: Bolsas no Exterior - Pesquisa
• Processo FAPESP: 15/16038-2 - Estimativas do tipo Lp-Lq para Operadores de Evolução
• Beneficiário: Marcelo Rempel Ebert
• Modalidade de apoio: Auxílio à Pesquisa - Regular