We consider a class of second-order linear nonautonomous parabolic equations in ℝd with time periodic unbounded coefficients. We give sufficient conditions for the evolution operator G(t, s) be compact in C b(ℝd) for t > s, and describe the asymptotic behavior of G(t, s)f as t – s → ∞ in terms of a family of measures μs, s ϵ ℝ, solution of the associated Fokker-Planck equation.
Compactness and asymptotic behavior in nonautonomous linear parabolic equations with unbounded coefficients in ℝd / Lunardi, A.. - STAMPA. - 80:(2011), pp. 447-461. [10.1007/978-3-0348-0075-4_23]
Compactness and asymptotic behavior in nonautonomous linear parabolic equations with unbounded coefficients in ℝd
Lunardi A.
2011-01-01
Abstract
We consider a class of second-order linear nonautonomous parabolic equations in ℝd with time periodic unbounded coefficients. We give sufficient conditions for the evolution operator G(t, s) be compact in C b(ℝd) for t > s, and describe the asymptotic behavior of G(t, s)f as t – s → ∞ in terms of a family of measures μs, s ϵ ℝ, solution of the associated Fokker-Planck equation.File in questo prodotto:
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