Asymptotic stability of a linear Boltzmann-type equation
Volume 41 / 2014
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.
