On invariant measures associated to weakly coupled systems of Kolmogorov equations

2017/05/10 by Davide Addona, Addona, Davide, Luciana Angiuli +3
Mathematics · #35B40 (Secondary) #35K40 (Primary) #35K45 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35B40 #msc:35K40 #msc:35K45

paper · pdf · doi:10.48550/arxiv.1705.03784

arxiv created 2017/05/10 · arxiv updated 2017/05/11

Abstract

In this paper, we deal with weakly coupled elliptic systems \boldsymbol\mathcal A with unbounded coefficients. We prove the existence and characterize all the systems of invariant measures for the semigroup (\bf T(t))_{t≥ 0} associated to \boldsymbol\mathcal A in C_b(\mathbb R^d;\mathbb R^m). We also show some relevant properties of the extension of (\bf T(t))_{t≥ 0} to the L^p-spaces related to systems of invariant measures. Finally, we study the asymptotic behaviour of (\bf T(t))_{t≥ 0} as t tends to +∞.

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