Convexity breaking of the free boundary for porous medium equations
Kazuhiro Ishige, Paolo Salani · Interfaces and Free Boundaries Mathematical Analysis Computation and Applications · 2010
We investigate the preservation of convexity of the free boundary by the solutions of the porous medium equation. We prove that starting with an initial datum with some kind of suboptimal αconcavity property, the convexity of the positivity set can be lost in a short time.