Invariant Borel Probability Measures And Statistical Solution Of Discrete Three-component Reversible Gray-scott Model

This master's thesis studies the asymptotic behavior of the solution of the non-autonomous three-component reversible Gray-Scott equation system on an infinite lattice point.First of all,the thesis proves the existence,uniqueness and boundedness of the solution of the lattice point equation system,and the solution operator generates a continuous process,which has a bounded pullback absorption set and has a pullback asymptotic compactness,which proves that there is a pullback attractor in the continuous process of generation.Then,the paper proves that there is ? continuity in the process of generating the solution operator,combined with the existence of the pullback attractor,the invariant Borel probability measure is obtained,and further prove that the invariant measure is a statistical solution,so as to prove the existence of the statistical solution,and finally proves that the statistical solution satisfies the Liouville-type theorem.