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Indefinite metrics and dichotomy of solutions of linear differential equations in Hilbert spaces. (English) Zbl 0855.34068

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.

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
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