Ultracontractivity and Gaussian bounds for evolution families associated with nonautonomous forms |
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| Authors: | Hafida Laasri Delio Mugnolo |
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| Institution: | 1. Arbeitsgruppe Funktionalanalysis, Fakultät Mathematik und Informatik, Universität Wuppertal, Wuppertal, Germany;2. Lehrgebiet Analysis, Fakultät Mathematik und Informatik, FernUniversität in Hagen, Hagen, Germany |
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| Abstract: | We develop a variational approach in order to study qualitative properties of nonautonomous parabolic equations. Based on the method of product integrals, we discuss invariance properties and ultracontractivity of evolution families in Hilbert space. Our main results give sufficient conditions for the heat kernel of the evolution family to satisfy Gaussian-type bounds. Along the way, we study examples of nonautonomous equations on graphs, metric graphs, and domains. |
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| Keywords: | evolution families kernel estimates nonautonomous parabolic problems |
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