In this paper, we find the critical exponent for the existence of global small data solutions to: [Formula presented]in the case of so-called non-effective damping, θ∈(σ,2σ], where σ≠1 and f=|u|α or f=|ut|α, in low space dimension. By critical exponent we mean that global small data solution exists for supercritical powers α>α̃ and do not exist, in general, for subcritical powers 1ᾱ, but we leave open to determine if a counterpart nonexistence result for α holds or not.
The critical exponent for semilinear σ-evolution equations with a strong non-effective damping
D'Abbicco M.
;
2022-01-01
Abstract
In this paper, we find the critical exponent for the existence of global small data solutions to: [Formula presented]in the case of so-called non-effective damping, θ∈(σ,2σ], where σ≠1 and f=|u|α or f=|ut|α, in low space dimension. By critical exponent we mean that global small data solution exists for supercritical powers α>α̃ and do not exist, in general, for subcritical powers 1ᾱ, but we leave open to determine if a counterpart nonexistence result for α holds or not.File in questo prodotto:
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DAE_NLA critical exp Postprint.pdf
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DAbbicco Ebert 2022 Nonlinear An.pdf
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