The critical exponent for semilinear <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e22" altimg="si17.svg"><mml:mi>σ</mml:mi></mml:math>-evolution equations with a strong non-effective damping

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&gt;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.

Topics & Concepts