### Regularity and time behavior of the solutions of linear and quasilinear parabolic equations

Maria Michaela Porzio

#### Abstract

In this paper, we study the regularity, the uniqueness and the asymptotic behavior of the solutions to a class of nonlinear operators in dependence of the summability properties of the datum $f$ and of the initial datum $u_0$. The case of only summable data $f$ and $u_0$ is allowed. We prove that these equations satisfy surprising regularization phenomena. Moreover, we prove estimates (depending continuously from the data) that for zero datum $f$ become well known decay (or ultracontractive) estimates.

#### Article information

Source
Adv. Differential Equations Volume 23, Number 5/6 (2018), 329-372.

Dates
First available in Project Euclid: 23 January 2018