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arXiv · 2009.04388

Lifespan estimates for local solutions to the semilinear wave equation in Einstein-de Sitter spacetime

Alessandro Palmieri
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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.

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Alessandro Palmieri. 2020-09-09. Lifespan estimates for local solutions to the semilinear wave equation in Einstein-de Sitter spacetime. https://doi.org/10.1080/00036811.2022.2088529

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