We consider a general time-periodic linear transport equation with integral source term and we prove the existence of a Floquet principal eigenvalue, namely a real number such that the equation rescaled by this number admits positive periodic solutions. We also prove the exponential attractiveness of these solutions. The method relies on general spectral results about positive operators.
35B10 ; 35B40 ; 35Q92 ; 35R01 ; 47B65
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