Asymptotic behavior for two-dimensional, quasi-autonomous, almost- periodic evolution equations (Q579496)

Let A be a maximal monotone operator in the two dimensional space \(R^ 2\) and let \(f(t): R\to R^ 2\) be a measurable function which is \(S^ 1\)-almost periodic. It is proved that if u is any solution of the evolution equation (1) \(\dot u(t)+Au(t)\ni f(t)\) which is bounded on \(R^+\), then \(u(t): R^+\to R^ 2\) is asymptotic for \(t\to \infty\) to an almost periodic solution of the equation (1). [A relevant basic reference is: the author, Nonlinear evolution equation-global behavior of solutions, Lect. Notes Math. 841 (1981; Zbl 0461.35002)].