Quenching phenomenon of singular parabolic problems with L^1 initial data

Abstract

We extend some previous existence results for quenching type parabolic problems involving a negative power of the unknown in the equation to the case of merely integrable initial data. We show that $L^1(\Omega)$ is the suitable framework to obtain the continuous dependence with respect to some norm of the initial datum; This way we answer to the question raised by several authors in the previous literature. We also show the complete quenching phenomena for such a L^1-initial datum.

Keywords

• Quenching type parabolic equations
• L^1-initial datum
• free boundary