Speaker
Giacomo Ageno, University of Cambridge
Abstract
We consider the singularity formation for the classical one-phase Stefan problem in two space dimensions, describing the melting of an ice body surrounded by water. For radial ice disks, Herrero and Velázquez derived the Type II melting laws, and Hadžić and Raphaël later analyzed their stability. However, the melting problem is genuinely nonradial: formal asymptotic of Andreucci, Herrero and Velázquez predicts that compact melting regions should asymptotically collapse onto ellipses. We study the nonradial stability for this elliptic type II melting scenario. Starting with regular data and interface close to an ellipse, the solution melts in finite time with rescaled boundary converging to an ellipse selected by the data. The strategy involves a Lyapunov-Schmidt reduction around the manifold of shrinking elliptic profiles. This is based on work in progress with M. Hadžić and P. Raphaël.
Giacomo Ageno, University of Cambridge
Abstract
We consider the singularity formation for the classical one-phase Stefan problem in two space dimensions, describing the melting of an ice body surrounded by water. For radial ice disks, Herrero and Velázquez derived the Type II melting laws, and Hadžić and Raphaël later analyzed their stability. However, the melting problem is genuinely nonradial: formal asymptotic of Andreucci, Herrero and Velázquez predicts that compact melting regions should asymptotically collapse onto ellipses. We study the nonradial stability for this elliptic type II melting scenario. Starting with regular data and interface close to an ellipse, the solution melts in finite time with rescaled boundary converging to an ellipse selected by the data. The strategy involves a Lyapunov-Schmidt reduction around the manifold of shrinking elliptic profiles. This is based on work in progress with M. Hadžić and P. Raphaël.