A note on the nonexistence of global solutions to the semilinear wave equation with nonlinearity of derivative-type in the generalized Einstein-de Sitter spacetime

Makram Hamouda; Mohamed Ali Hamza; Alessandro Palmieri

doi:10.3934/cpaa.2021127

Article Contents

2021, Volume 20, Issue 11: 3703-3721. Doi: 10.3934/cpaa.2021127 open access

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A note on the nonexistence of global solutions to the semilinear wave equation with nonlinearity of derivative-type in the generalized Einstein-de Sitter spacetime

1.
Basic Sciences Department, Deanship of Preparatory Year and Supporting Studies, P. O. Box 1982, Imam Abdulrahman Bin Faisal University, Dammam, KSA
2.
Department of Mathematics, University of Pisa, Largo B. Pontecorvo 5, 56127 Pisa, Italy

^* Corresponding author
^* Corresponding author

Received: January 31, 2021

Revised: May 31, 2021

Early access: July 2021

Published: November 2021

The third author is supported by the GNAMPA project 'Problemi stazionari e di evoluzione nelle equazioni di campo nonlineari dispersive'

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Abstract

In this paper, we establish blow-up results for the semilinear wave equation in generalized Einstein-de Sitter spacetime with nonlinearity of derivative type. Our approach is based on the integral representation formula for the solution to the corresponding linear problem in the one-dimensional case, that we will determine through Yagdjian's Integral Transform approach. As upper bound for the exponent of the nonlinear term, we discover a Glassey-type exponent which depends both on the space dimension and on the Lorentzian metric in the generalized Einstein-de Sitter spacetime.

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Mathematics Subject Classification: Primary: 35B44, 35C15, 35L71; Secondary: 35A08, 35B33, 35L15.

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