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

communications on pure and applied analysis

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