Ultracontractivity and Gaussian bounds for evolution families associated with non-autonomous forms
Analysis of PDEs
2020-12-14 v2
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.
Keywords
Cite
@article{arxiv.1811.03705,
title = {Ultracontractivity and Gaussian bounds for evolution families associated with non-autonomous forms},
author = {Hafida Laasri and Delio Mugnolo},
journal= {arXiv preprint arXiv:1811.03705},
year = {2020}
}