Nonexistence of global solutions to the Euler–Poisson–Darboux equation in Rn: Subcritical case

Abstract

The singular Cauchy problem for the semilinear Euler–Poisson–Darboux equation in $R^n$ with power type nonlinearity is studied in this paper. We show that the blow up power is related to the Strauss exponent, which generalizes the blow up result from the regular semilinear wave equation with scale invariant damping to the corresponding singular problem, and hence give some affirmative answer partially to the open problem posed by D’Abbicco in a recent paper.