Differential and Integral Equations

Strong convergence of bounded sequences of solutions of porous medium equations

Gary M. Lieberman

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 show that smooth solutions of porous medium equations satisfy a simple $L^2$ gradient estimate on sets where the solution itself is small. Along with known continuity estimates for solutions and an estimate on second derivatives of smooth solutions, this estimate allows us to show that approximating smooth solutions of a porous medium equation converge strongly to the weak solution.

Article information

Differential Integral Equations, Volume 11, Number 3 (1998), 395-407.

First available in Project Euclid: 30 April 2013

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K65: Degenerate parabolic equations
Secondary: 35B05: Oscillation, zeros of solutions, mean value theorems, etc. 35B45: A priori estimates 76S05: Flows in porous media; filtration; seepage


Lieberman, Gary M. Strong convergence of bounded sequences of solutions of porous medium equations. Differential Integral Equations 11 (1998), no. 3, 395--407. https://projecteuclid.org/euclid.die/1367341059

Export citation