scholarly journals 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

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Makram Hamouda ◽  
Mohamed Ali Hamza ◽  
Alessandro Palmieri
Keyword(s):  
Wave Equation ◽  
Blow Up ◽  
Integral Transform ◽  
Global Solutions ◽  
Representation Formula ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Semilinear Wave Equation ◽  
Sitter Spacetime ◽  
Derivative Type

<p style='text-indent:20px;'>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.</p>

scholarly journals Lifespan of solutions to wave equations in de Sitter spacetime

2018 ◽  
Vol 148 (6) ◽  
pp. 1313-1330 ◽  
Author(s):  
Weiping Yan
Keyword(s):  
Wave Equation ◽  
Nonlinear Wave Equation ◽  
Finite Time ◽  
Wave Equations ◽  
Blow Up ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Sitter Spacetime ◽  
Image Position ◽  
Lifespan Estimate

We consider the finite-time blow-up of solutions for the following two kinds of nonlinear wave equation in de Sitter spacetime:This proof is based on a new blow-up criterion, which generalizes that by Sideris. Furthermore, we give the lifespan estimate of solutions for the problems.

scholarly journals Finite lifespan of solutions of the semilinear wave equation in the Einstein–de Sitter spacetime

2019 ◽  
Vol 32 (07) ◽  
pp. 2050018 ◽  
Author(s):  
Anahit Galstian ◽  
Karen Yagdjian
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Wave Equation ◽  
De Sitter Spacetime ◽  
Quantum Field ◽  
De Sitter ◽  
Semilinear Wave Equation ◽  
Sitter Spacetime ◽  
Text Model ◽  
De Sitter Universe

We examine the solutions of the semilinear wave equation, and, in particular, of the [Formula: see text] model of quantum field theory in the curved spacetime. More exactly, for [Formula: see text] we prove that the solution of the massless self-interacting scalar field equation in the Einstein–de Sitter universe has finite lifespan.

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