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Blow-up results for semilinear damped wave equations in Einstein–de Sitter spacetime

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Abstract

We prove by using an iteration argument some blow-up results for a semilinear damped wave equation in generalized Einstein–de Sitter spacetime with a time-dependent coefficient for the damping term and power nonlinearity. Then, we conjecture an expression for the critical exponent due to the main blow-up results, which is consistent with many special cases of the considered model and provides a natural generalization of Strauss exponent. In the critical case, we consider a non-autonomous and parameter dependent Cauchy problem for a linear ODE of second order, whose explicit solutions are determined by means of special functions’ theory.

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Acknowledgements

A. Palmieri is supported by the GNAMPA project ‘Problemi stazionari e di evoluzione nelle equazioni di campo nonlineari dispersive’. The author would like to thank Karen Yagdjian (UTRGV), who first introduced him to the model considered in this work.

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  1. Department of Mathematics, University of Pisa, Largo B. Pontecorvo 5, 56127, Pisa, Italy

    Alessandro Palmieri

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Palmieri, A. Blow-up results for semilinear damped wave equations in Einstein–de Sitter spacetime. Z. Angew. Math. Phys. 72, 64 (2021). https://doi.org/10.1007/s00033-021-01494-x

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