Compactness and Asymptotic Behavior in Nonautonomous Linear Parabolic Equations with Unbounded Coefficients in ℝ d

Alessandra Lunardi

doi:10.1007/978-3-0348-0075-4_23

Compactness and Asymptotic Behavior in Nonautonomous Linear Parabolic Equations with Unbounded Coefficients in ℝ d

Alessandra Lunardi

https://doi.org/10.1007/978-3-0348-0075-4_23

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Publication Date: Jan 1, 2011

Citations: 16

Affiliation: University of Parma

#Linear Parabolic Equations #Unbounded Coefficients + Show 8 more

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Abstract

AbstractWe 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.KeywordsEvolution operatorcompactnessasymptotic behavior.

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