Lifespan estimates for local solutions to the semilinear wave equation in Einstein-de Sitter spacetime
Analysis of PDEs
2022-06-22 v1
Abstract
In this paper, we prove some blow-up results for the semilinear wave equation in generalized Einstein-de Sitter spacetime by using an iteration argument and we derive upper bound estimates for the lifespan. In particular, we will focus on the critical cases which require the employment of a slicing procedure in the iterative mechanism. Furthermore, in order to deal with the main critical case, we will introduce a non-autonomous and parameter-dependent Cauchy problem for a linear ODE of second-order, whose explicit solution will be determined by applying the theory of special functions.
Keywords
Cite
@article{arxiv.2009.04388,
title = {Lifespan estimates for local solutions to the semilinear wave equation in Einstein-de Sitter spacetime},
author = {Alessandro Palmieri},
journal= {arXiv preprint arXiv:2009.04388},
year = {2022}
}