Strong convergence of bounded sequences of solutions of porous medium equations
Gary M. Lieberman · Differential and Integral Equations · 1998
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.