Hypercontractivity, supercontractivity, ultraboundedness and stability in semilinear problems
Analysis of PDEs
2016-07-19 v1
Abstract
We study the Cauchy problem associated to a family of nonautonomous semilinear equations in the space of bounded and continuous functions over R^d and in L^p-spaces with respect to tight evolution systems of measures. Here, the linear part of the equation is a nonautonomous second-order elliptic operator with unbounded coefficients defined in IxR^d, (I being a right-halfline). To the above Cauchy problem we associate a nonlinear evolution operator, which we study in detail, proving some summability improving properties. We also study the stability of the null solution to the Cauchy problem.
Cite
@article{arxiv.1607.05247,
title = {Hypercontractivity, supercontractivity, ultraboundedness and stability in semilinear problems},
author = {Davide Addona and Luciana Angiuli and Luca Lorenzi},
journal= {arXiv preprint arXiv:1607.05247},
year = {2016}
}