Khatskevich, Victor; Zelenko, Leonid Indefinite metrics and dichotomy of solutions of linear differential equations in Hilbert spaces. (English) Zbl 0855.34068 Chin. J. Math. 24, No. 2, 99-112 (1996). The authors study nonautonomous linear differential equations \(\dot u(t) = A(t) u(t)\) with unbounded operators \(A(t)\) on a Hilbert space and obtain dichotomic behavior using Lyapunov type functionals. The result is applied to a nonautonomous diffusion equation. Reviewer: R.Nagel (Tübingen) Cited in 4 Documents MSC: 34G10 Linear differential equations in abstract spaces 47N20 Applications of operator theory to differential and integral equations 35B40 Asymptotic behavior of solutions to PDEs 35K20 Initial-boundary value problems for second-order parabolic equations Keywords:nonautonomous linear differential equations; Hilbert space; dichotomic behavior; nonautonomous diffusion equations PDFBibTeX XMLCite \textit{V. Khatskevich} and \textit{L. Zelenko}, Chin. J. Math. 24, No. 2, 99--112 (1996; Zbl 0855.34068)