The critical exponent for semilinear wave equations with damped oscillations

Marcello D'Abbicco

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arXiv · 2608.11722

The critical exponent for semilinear wave equations with damped oscillations

Marcello D'Abbicco

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Abstract

We determine the existence exponent for the global small data solutions for a class of evolution equations with power nonlinearity under the effect of a dissipation that dampen the oscillations at low frequencies and produce overdamping at high frequencies. In the case of the wave equation with viscoelastic dissipation, the counterpart of blow-up in space dimension $n=3$ has been very recently proved by Wenhui Chen, showing that the existence exponent is optimal.

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Marcello D'Abbicco. 2026-08-12. The critical exponent for semilinear wave equations with damped oscillations. https://arxiv.org/abs/2608.11722

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