Asymptotic behavior in time periodic parabolic problems with unbounded coefficients

2009/08/08 by Luca Lorenzi, Lorenzi, L., Alessandra Lunardi +3 · 1 citation
Computer Science · Engineering · #35B65 #47D06 #47F05 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.0908.1170

openalex publication_date 2009/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study asymptotic behavior in a class of non-autonomous second order parabolic equations with time periodic unbounded coefficients in \mathbb R× \mathbb R^d. Our results generalize and improve asymptotic behavior results for Markov semigroups having an invariant measure. We also study spectral properties of the realization of the parabolic operator u↦ \cal A(t) u - u_t in suitable L^p spaces.

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