Advances in Differential Equations

Fujita type results for a class of degenerate parabolic operators

Andrea Pascucci

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 global existence of non-negative solutions to the Cauchy problem for $Lu= - u^{p}$ where $L$ belongs to a class ${\cal L}$ of hypoelliptic operators of degenerate parabolic type and $p>1$. Extending some old results by Fujita, we prove the existence and we determine explicitly a critical exponent $p^{*}$ for the problem. Namely, we prove that if $p>p^{*}$ then there are global positive solutions to the problem, while if $1 <p<p^{*}$ then all non-trivial solutions blow up in finite time. We also study the critical case $p=p^{*}$ for a remarkable subclass of ${\cal L}$.

Article information

Source
Adv. Differential Equations Volume 4, Number 5 (1999), 755-776.

Dates
First available in Project Euclid: 15 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.ade/1366030979

Mathematical Reviews number (MathSciNet)
MR1696353

Zentralblatt MATH identifier
0978.35024

Subjects
Primary: 35B33: Critical exponents
Secondary: 35H10: Hypoelliptic equations 35K65: Degenerate parabolic equations

Citation

Pascucci, Andrea. Fujita type results for a class of degenerate parabolic operators. Adv. Differential Equations 4 (1999), no. 5, 755--776. https://projecteuclid.org/euclid.ade/1366030979.


Export citation