Open AccessStatistical solution and Liouville type theorem for coupled Schrödinger-Boussinesq equations on infinite lattices
Author(s) -
Congcong Li,
Chunqiu Li,
Jintao Wang
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2021311
Subject(s) - mathematics , attractor , type (biology) , invariant (physics) , lattice (music) , pure mathematics , mathematical physics , mathematical analysis , physics , ecology , acoustics , biology
In this article, we are concerned with statistical solutions for the nonautonomous coupled Schrödinger-Boussinesq equations on infinite lattices. Firstly, we verify the existence of a pullback- \begin{document}$ {\mathcal{D}} $\end{document} attractor and establish the existence of a unique family of invariant Borel probability measures carried by the pullback- \begin{document}$ {\mathcal{D}} $\end{document} attractor for this lattice system. Then, it will be shown that the family of invariant Borel probability measures is a statistical solution and satisfies a Liouville type theorem. Finally, we illustrate that the invariant property of the statistical solution is indeed a particular case of the Liouville type theorem.