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Asymptotic stability of a linear Boltzmann-type equation

Volume 41 / 2014

Roksana Brodnicka, Henryk Gacki Applicationes Mathematicae 41 (2014), 323-334 MSC: Primary 47D07, 47N20; Secondary 45K05, 28A33, 60H10. DOI: 10.4064/am41-4-3

Abstract

We present a new necessary and sufficient condition for the asymptotic stability of Markov operators acting on the space of signed measures. The proof is based on some special properties of the total variation norm. Our method allows us to consider the Tjon–Wu equation in a linear form. More precisely a new proof of the asymptotic stability of a stationary solution of the Tjon–Wu equation is given.

Authors

  • Roksana BrodnickaInstitute of Mathematics
    Silesian University
    Bankowa 14
    40-007 Katowice, Poland
    e-mail
  • Henryk GackiInstitute of Mathematics
    Silesian University
    Bankowa 14
    40-007 Katowice, Poland
    e-mail

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