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 with a combination of spatial derivatives up to the second order that we deffine 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.
Local existence in free interface problems with underlying second-order Stefan condition / BRAUNER CLAUDE, Michel; Lorenzi, Luca Francesco Giuseppe. - In: REVUE ROUMAINE DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 0035-3965. - 63:4(2018), pp. 339-359.
Local existence in free interface problems with underlying second-order Stefan condition
LORENZI LUCA FRANCESCO GIUSEPPE
2018-01-01
Abstract
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 with a combination of spatial derivatives up to the second order that we deffine 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
