Advances in Differential Equations

Pointwise decay for the solutions of degenerate and singular parabolic equations

Petri Juutinen and Peter Lindqvist

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


We study the asymptotic behavior, as $t\to\infty$, of the solutions to the evolutionary $p$-Laplace equation \[ v_t={\operatorname{div}}( | {\nabla v} | ^{p-2}\nabla v), \] with time-independent lateral boundary values. We obtain the sharp decay rate of $\max_{x\in{\Omega}} | {v(x,t)-u(x)}| $, where $u$ is the stationary solution, both in the degenerate case $p > 2$ and in the singular case $1 < p > 2$. A key tool in the proofs is the Moser iteration, which is applied to the difference $v(x,t)-u(x)$. In the singular case, we construct an example proving that the celebrated phenomenon of finite extinction time, valid for $v(x,t)$ when $u\equiv 0$, does not have a counterpart for $v(x,t)-u(x)$.

Article information

Adv. Differential Equations Volume 14, Number 7/8 (2009), 663-684.

First available in Project Euclid: 18 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K55: Nonlinear parabolic equations 35K65: Degenerate parabolic equations 35B40: Asymptotic behavior of solutions


Juutinen, Petri; Lindqvist, Peter. Pointwise decay for the solutions of degenerate and singular parabolic equations. Adv. Differential Equations 14 (2009), no. 7/8, 663--684.

Export citation