Solvability of some Stefan type problems

TL;DR

This paper investigates the solvability of certain Stefan type problems, establishing existence and uniqueness of solutions within anisotropic Sobolev spaces for data in L^1, using renormalized truncations and generalized monotonicity methods.

Contribution

It introduces new existence and uniqueness results for Stefan problems with L^1 data in anisotropic Sobolev spaces, employing advanced functional analysis techniques.

Findings

Proved existence of renormalized solutions.

Established uniqueness of solutions.

Applied generalized monotonicity method.

Abstract

In this paper, we interest on some class of Stefan type problems. We prove the existence and uniqueness of renormalized solution in anisotropic Sobolev spaces with data belongs to $L^1- data,$ based on the properties of the renormalized trunctions and the generalized monotonicity method in the functional spaces.