Advances in Differential Equations

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

Maria Michaela Porzio

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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

Permanent link to this document
https://projecteuclid.org/euclid.ade/1516676481

Subjects
Primary: 35K10: Second-order parabolic equations 35K59: Quasilinear parabolic equations 35D30: Weak solutions

Citation

Porzio, Maria Michaela. Regularity and time behavior of the solutions of linear and quasilinear parabolic equations. Adv. Differential Equations 23 (2018), no. 5/6, 329--372. https://projecteuclid.org/euclid.ade/1516676481


Export citation