LOCAL EXISTENCE IN FREE INTERFACE PROBLEMS WITH UNDERLYING SECOND-ORDER STEFAN CONDITION
Claude-Michel Brauner, Luca Lorenzi · HAL (Le Centre pour la Communication Scientifique Directe) · 2018
In this survey we consider free interface problems that do not fall within the class of Stefan problems, as there is no specific condition on the velocity of the interface. At least near some equilibrium, we are able to associate the velocity to a combination of spatial derivatives up to the second order that we define as a second-order Stefan condition. Then, we may reformulate the system as a fully nonlinear problem, for which it holds local in time existence and uniqueness.