Differential and Integral Equations

Strong convergence of bounded sequences of solutions of porous medium equations

Gary M. Lieberman

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Abstract

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

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

Dates
First available in Project Euclid: 30 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1367341059

Mathematical Reviews number (MathSciNet)
MR1745546

Zentralblatt MATH identifier
1007.35109

Subjects
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

Citation

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


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