Strong convergence of solutions to nonautonomous Kolmogorov equations
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- by Luca Lorenzi, Alessandra Lunardi and Roland Schnaubelt PDF
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Abstract:
We study a class of nonautonomous, linear, parabolic equations with unbounded coefficients on $\mathbb {R}^{d}$ which admit an evolution system of measures. It is shown that the solutions of these equations converge to constant functions as $t\to +\infty$. We further establish the uniqueness of the tight evolution system of measures and treat the case of converging coefficients.References
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Additional Information
- Luca Lorenzi
- Affiliation: Dipartimento di Matematica e Informatica, Università degli Studi di Parma, Parco Area delle Scienze 53/A, I-43124 Parma, Italy
- MR Author ID: 649239
- Email: luca.lorenzi@unipr.it
- Alessandra Lunardi
- Affiliation: Dipartimento di Matematica e Informatica, Università degli Studi di Parma, Parco Area delle Scienze 53/A, I-43124 Parma, Italy
- MR Author ID: 116935
- Email: alessandra.lunardi@unipr.it
- Roland Schnaubelt
- Affiliation: Department of Mathematics, Karlsruhe Institute of Technology, D-76128 Karlsruhe, Germany
- MR Author ID: 603222
- Email: schnaubelt@kit.edu
- Received by editor(s): August 17, 2015
- Received by editor(s) in revised form: November 6, 2015
- Published electronically: April 28, 2016
- Additional Notes: The first author wishes to thank the Department of Mathematics of the Karlsruhe Institute of Technology for the kind hospitality during his visit.
This work was supported by the M.I.U.R. Research Project PRIN 2010-2011 “Problemi differenziali di evoluzione: approcci deterministici e stocastici e loro interazioni” - Communicated by: Joachim Krieger
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 3903-3917
- MSC (2010): Primary {35K10; Secondary 35K15, 35B40}
- DOI: https://doi.org/10.1090/proc/13031
- MathSciNet review: 3513547