arXiv subjects

Sabrina D. Roscani

Publications and source records attributed to Sabrina D. Roscani.

4 recordsLinked to original sources

arXiv2021

About the Convergence of a Family of Initial Boundary Value Problems for a Fractional Diffusion Equation with Robin Conditions

We consider a family of initial boundary value problems governed by a fractional diffusion equation with Caputo derivative in time, where the parameter is the Newton heat transfer coefficient linked to the Robin condition on the boundary. For each problem we prove existence and uniqueness of solution by a Fourier approach. This will enable us to also prove the convergence of the family of solutions to the solution of the limit problem, which is obtained by replacing the Robin boundary condition with a Dirichlet boundary condition.

math.AP↗

arXiv2018

Two different fractional Stefan problems which are convergent to the same classical Stefan problem

Two fractional Stefan problems are considered by using Riemann-Liouville and Caputo derivatives of order $α\in (0,1)$ such that in the limit case ($α=1$) both problems coincide with the same classical Stefan problem. For the one and the other problem, explicit solutions in terms of the Wright functions are presented. We prove that these solutions are different even though they converge, when $α\nearrow 1$, to the same classical solution. This result also shows that some limits are not commutative when fractional derivatives are used.

math.AP↗

arXiv2015

A Generalization of the Hopf's Lemma for the 1-D Moving-Boundary Problem for the Fractional Diffusion Equation and its Application to a Fractional Free-Boundary Problem

This paper deals with a theoretical mathematical analysis of a one-dimensional-moving-boundary problem for the time-fractional diffusion equation, where the time-fractional derivative of order $\al$ $\in (0,1)$ is taken in the Caputo's sense. A generalization of the Hopf's lemma is proved, and then this result is used to prove a monotonicity property for the free-boundary when a fractional free-boundary Stefan problem is considered.

math.AP↗

arXiv2014

A Generalized Neumann Solution for the Two-Phase Fractional Lamé-Clapeyron-Stefan Problem

We obtain a generalized Neumann solution for the two-phase fractional Lamé-Clapeyron-Stefan problem for a semi-infinite material with constant boundary and initial conditions. In this problem, the two governing equations and a governing condition for the free boundary include a fractional time derivative in the Caputo sense of order $0<\al\leq 1$. When $ \al \nearrow $ 1 we recover the classical Neumann solution for the two-phase Lamé-Clapeyron-Stefan problem given through the error function.

math.AP↗