Fujita modified exponent for scale invariant damped semilinear wave equations

Fujita modified exponent for scale invariant damped semilinear wave equations

The aim of this paper is to prove a blow-up result of the solution for a semilinear scale invariant damped wave equation under a suitable decay condition on radial initial data. The admissible range for the power of the nonlinear term depends both on the damping coefficient and on the pointwise deca...

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Veröffentlicht in:Journal of evolution equations 2021-06, Vol.21 (2), p.2735-2748
Hauptverfasser: Chiarello, Felisia Angela, Girardi, Giovanni, Lucente, Sandra
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Analysis
Damping
Decay rate
Invariants
Mathematics
Mathematics and Statistics
Upper bounds
Wave equations
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Girardi, Giovanni
Lucente, Sandra
description The aim of this paper is to prove a blow-up result of the solution for a semilinear scale invariant damped wave equation under a suitable decay condition on radial initial data. The admissible range for the power of the nonlinear term depends both on the damping coefficient and on the pointwise decay order of the initial data. In addition, we give an upper bound estimate for the lifespan of the solution. It depends not only on the exponent of the nonlinear term and not only on the damping coefficient but also on the size of the decay rate of the initial data.
doi_str_mv 10.1007/s00028-021-00705-2
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subjects Analysis
Damping
Decay rate
Invariants
Mathematics
Mathematics and Statistics
Upper bounds
Wave equations
title Fujita modified exponent for scale invariant damped semilinear wave equations
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