Blow Up of Solutions to Semilinear Wave Equations with Critical Exponent in High Dimensions*

Abstract

In this paper, the author considers the Cauchy problem for semilinear wave equations with critical exponent in n ≥ 4 space dimensions. Under some positivity conditions on the initial data, it is proved that there can be no global solutions no matter how small the initial data are.

Keywords

Semilinear wave equation / Critical exponent / Cauchy problem / Blow up / 35L05 / 35L70 / 35L15

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