arXiv subjects

María Fernanda Natale

Publications and source records attributed to María Fernanda Natale.

3 recordsLinked to original sources

arXiv2025

Relationship among solutions for three-phase change problems with Robin, Dirichlet, and Neumann boundary conditions

This study investigates the melting process of a three-phase Stefan problem in a semi-infinite material, imposing a convective boundary condition at the fixed face. By employing a similarity-type transformation, the problem is reduced to a solvable form, yielding a unique explicit solution. The analysis uncovers significant equivalences among the solutions of three different three-phase Stefan problems: one with a Robin boundary condition, another with a Dirichlet boundary condition, and a third one with a Neumann boundary condition at the fixed face. These equivalences are established under the condition that the problem data satisfy a specific relationship, providing new insights into the behaviour of phase change problems under varying boundary conditions.

math.AP↗

arXiv2020

Existence and uniqueness of the p-generalized modified error function

In this paper, the p-generalized modified error function is defined as the solution to a non-linear ordinary differential problem of second order with a Robin type condition at x=0. Existence and uniqueness of a non-negative C^\infty solution is proved by using a fixed point strategy. It is shown that the p-generalized modified error function converges to the p-modified error function defined as the solution to a similar problem with a Dirichlet condition at x=0. In both problems, for p=1, the generalized modified error function and the modified error function, studied recently in literature, are recovered. In addition, existence and uniqueness of solution to a problem with a Neumann condition is also analysed.

math.CA↗

arXiv2019

Existence and uniqueness of solution for two one-phase Stefan problems with variable thermal coefficients

One dimensional Stefan problems for a semi-infinite material with temperature dependent thermal coefficients are considered. Existence and uniqueness of solution are obtained imposing a Dirichlet or a Robin type condition at fixed face $x=0$. Moreover, it is proved that the solution of the problem with the Robin type condition converges to the solution of the problem with the Dirichlet condition at the fixed face. Computational examples are provided.

math.AP↗