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 μ s , \( s \in \mathbb{R} \), solution of the associated Fokker-Planck equation.
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Mathematics Subject Classification (2000). Primary 35D40; Secondary 28C10, 47D07.
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Lunardi, A. (2011). Compactness and Asymptotic Behavior in Nonautonomous Linear Parabolic Equations with Unbounded Coefficients in ℝd . In: Escher, J., et al. Parabolic Problems. Progress in Nonlinear Differential Equations and Their Applications, vol 80. Springer, Basel. https://doi.org/10.1007/978-3-0348-0075-4_23
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DOI: https://doi.org/10.1007/978-3-0348-0075-4_23
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