Ultracontractivity and Gaussian bounds for evolution families associated with non-autonomous forms
arXiv:1811.03705 · doi:10.1002/mma.5978
Abstract
We develop a variational approach in order to study the qualitative properties of non-autonomous parabolic equations. Based on the method of product integrals, we discuss long-time behavior, 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 non-autonomous equations on graphs, metric graphs, and domains.
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