Zhao, CaidiCaraballo Garrido, TomásLukaszewicz, Grzegorz2021-03-222021-03-222021-01-28Zhao, C., Caraballo Garrido, T. y Lukaszewicz, G. (2021). Statistical solution and Liouville type theorem for the Klein-Gordon-Schrödinger equations. Journal of Differential Equations, 281 (April), 1-1-32-32.0022-0396https://hdl.handle.net/11441/106412In this article, the authors investigate the system of Schr odinger and Klein-Gordon equations with Yukawa coupling. They rst prove the existence of pullback attractor and construct a family of invariant Borel probability measures. Then they establish that this family of probability measures satis es a Liouville type theorem and is indeed a statistical solution for the coupling equations. Further, they reveal that the invariant property of the statistical solution is a particular situation of the Liouville type theorem.application/pdf32 p.engAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Klein-Gordon-Schdinger equationsStatistical solutionPullback attractorInvariant measureLiouville type theoreminfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/10.1016/j.jde.2021.01.039