Differential and Integral Equations
- Differential Integral Equations
- Volume 11, Number 3 (1998), 395-407.
Strong convergence of bounded sequences of solutions of porous medium equations
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.
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