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May/June 2018 Regularity and time behavior of the solutions of linear and quasilinear parabolic equations
Maria Michaela Porzio
Adv. Differential Equations 23(5/6): 329-372 (May/June 2018).

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.

Citation

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Maria Michaela Porzio. "Regularity and time behavior of the solutions of linear and quasilinear parabolic equations." Adv. Differential Equations 23 (5/6) 329 - 372, May/June 2018.

Information

Published: May/June 2018
First available in Project Euclid: 23 January 2018

zbMATH: 06866843
MathSciNet: MR3749218

Subjects:
Primary: 35D30, 35K10, 35K59

Rights: Copyright © 2018 Khayyam Publishing, Inc.

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Vol.23 • No. 5/6 • May/June 2018
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