Statistical solution and Liouville type theorem for the Klein-Gordon-Schrödinger equations

2021 ◽  
Vol 281 ◽  
pp. 1-32
Author(s):  
Caidi Zhao ◽  
Tomás Caraballo ◽  
Grzegorz Łukaszewicz
Keyword(s):  
Type Theorem ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Liouville Type ◽  
Statistical Solution ◽  
Liouville Type Theorem ◽  
Klein Gordon

scholarly journals Statistical solution and Liouville type theorem for coupled Schrödinger-Boussinesq equations on infinite lattices

2022 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Congcong Li ◽  
Chunqiu Li ◽  
Jintao Wang
Keyword(s):  
Type Theorem ◽  
Boussinesq Equations ◽  
Probability Measures ◽  
Liouville Type ◽  
Statistical Solution ◽  
Liouville Type Theorem ◽  
The Family ◽  
Infinite Lattices ◽  
Borel Probability ◽  
Statistical Solutions

<p style='text-indent:20px;'>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-<inline-formula><tex-math id="M1">\begin{document}$ {\mathcal{D}} $\end{document}</tex-math></inline-formula> attractor and establish the existence of a unique family of invariant Borel probability measures carried by the pullback-<inline-formula><tex-math id="M2">\begin{document}$ {\mathcal{D}} $\end{document}</tex-math></inline-formula> 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.</p>

A Liouville Type Theorem for Poly-harmonic System with Dirichlet Boundary Conditions in a Half Space

2015 ◽  
Vol 15 (1) ◽  
Author(s):  
Zhao Liu ◽  
Wei Dai
Keyword(s):  
Boundary Conditions ◽  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Dirichlet Boundary ◽  
Type Theorem ◽  
Dirichlet Boundary Conditions ◽  
Liouville Type ◽  
Liouville Type Theorem ◽  
Harmonic System

AbstractIn this paper, we consider the following poly-harmonic system with Dirichlet boundary conditions in a half space ℝwherewhereis the Green’s function in ℝ

Sign in / Sign up

Export Citation Format

Share Document