# Adriana BriozzoNational Scientific and Technical Research Council, Rosario, Argentina · Matematica

Adriana Briozzo

PhD Mathematics

## About

42

Publications

3,137

Reads

**How we measure 'reads'**

A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more

322

Citations

Citations since 2016

Introduction

**Skills and Expertise**

## Publications

Publications (42)

We study a non-classical one phase Stefan problem with a particular control function which depends on the evolution of the temperature at the fixed face x=0 and, we assume a Neumann boundary condition and an over specified Robin condition at the fixed face. Under certain restrictions on the data an explicit similarity type solution is given. Moreov...

We consider a new Stefan-type problem for the classical heat equation with a latent heat and phase-change temperature depending of the variable time. We prove the equivalence of this Stefan problem with a class of boundary value problems for the nonlinear canonical evolution equation involving a source term with two free boundaries. This equivalenc...

In this article we study a mathematical model of the heat transfer in semi infinite material with a variable cross section, when the radial component of the temperature gradient can be neglected in comparison with the axial component is considered. In particular, the temperature distribution in liquid and solid phases of such kind of body can be mo...

Different one-phase Stefan problems for a semi-infinite slab are considered, involving a moving phase change material as well as temperature dependent thermal coefficients. Existence of at least one similarity solution is proved imposing a Dirichlet, Neumann, Robin or radiative–convective boundary condition at the fixed face. The velocity that aris...

A one-dimensional Stefan problem with spherical symmetry corresponding to the evaporation process of a droplet is considered. An equivalent integral formulation is obtained, and through a fixed point theorem, the existence and uniqueness of the solution are proved.

A solidification process for a semi-infinite material is presented through a non-linear two-phase unidimensional Stefan problem, where a convective boundary condition is imposed at the fixed face x=0. The volumetric heat capacity and the thermal conductivity are non-linear functions of the temperature in both solid and liquid phases and they verify...

Different one-phase Stefan problems for a semi-infinite slab are considered, involving a moving phase change material as well as temperature dependent thermal coefficients. Existence of at least one similarity solution is proved imposing a Dirichlet, Neumann, Robin or radiative-convective boundary condition at the fixed face. The velocity that aris...

Resumen: Se estudia un problema de Stefan a una fase para un líquido superenfriado con conductividad térmica dependiente de la temperatura. Se dan condiciones suficientes sobre los datos para obtener solución exacta de tipo similaridad, local en el tiempo y con blow-up en tiempo finito. La solución explícita se obtiene a través de laúnica solución...

We consider a supercooled one-dimensional Stefan problem with a Neumann boundary
condition and a variable thermal diffusivity. We establish a necessary and sufficient
condition for the heat flux at the fixed face x=0,
in order to obtain existence and uniqueness of a similarity type solution.
Moreover we over-specified the fixed face x=0 by a Dirich...

We consider a two‐phase Stefan problem for a semi‐infinite body x>0, with a convective boundary condition including a density jump at the free boundary with a time‐dependent heat transfer coefficient of the type h/t, h>0 whose solution was given in D. A. Tarzia, PAMM. Proc. Appl. Math. Mech. 7, 1040307–1040308 (2007). We demonstrate that the soluti...

One-dimensional free boundary problem for a nonlinear diffusion - convection equation with a Dirichlet condition at fixed face $x=0$, variable in time, is considered. Throught several transformations the problem is reduced to a free boundary problem for a diffusion equation and the integral formulation is obtained. By using fixed point theorems, th...

One-dimensional free boundary problem for a nonlinear diffusion–convection equation with a Dirichlet condition at fixed face x=0, variable in time, is considered. Through several transformations the problem is reduced to a free boundary problem for a diffusion equation and the integral formulation is obtained. By using fixed point theorems, the exi...

On the paper D. Burini, S De Lillo, G. Fioriti, Acta Mech.,
229 No. 10 (2018), pp 4215–4228.
It is a letter to the Editor (3 pages).

A supercooled one-dimensional Stefan problem with a Neumann boundary condition and a variable thermal diffusivity is considered. Necessary and sufficient conditions on the data of problem and on the heat flux at the fixed face x = 0 are established to have existence and uniqueness of similarity type solution which is obtained from solution of an eq...

A non-classical one dimensional Stefan problem with thermal coefficients temperature dependent and a Robin type condition at fixed face x=0 for a semi-infinite material is considered. The source function depends on the evolution the heat flux at the fixed face x=0. Existence of a similarity type solution is obtained and the asymptotic behaviour of...

We consider a nonlinear one-dimensional Stefan problem for a semi-infinite material \(x>0,\) with phase change temperature \(T_{f}.\) We assume that the heat capacity and the thermal conductivity satisfy a Storm’s condition. A convective boundary condition and a heat flux over-specified condition on the fixed face \(x=0\) are considered. Unknown th...

We study the supercooled one-phase Stefan problem for a semi-infinite material with temperature-dependent thermal conductivity at the fixed face x=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargi...

We consider a nonlinear one-dimensional Stefan problem for a semi-infinite material x > 0, with phase change temperature Tf. We assume that the heat capacity and the thermal conductivity satisfy a Storm’s condition, and we assume a convective boundary condition at the fixed face x = 0. A unique explicit solution of similarity type is obtained. More...

We study a one-phase Stefan problem for a semi-infinite material with temperature-dependent thermal conductivity with a boundary condition of Robin type at the fixed face

We consider two one-phase nonlinear one-dimensional Stefan problems for a semi-infinite material x>0, with phase change temperature T f . We assume that the heat capacity and the thermal conductivity satisfy a Storm’s condition. In the first case, we assume a heat flux boundary condition of the type q(t)=q0 t, and in the second case, we assume a te...

The mathematical analysis of two one-phase unidimensional and non-classical Stefan problems with nonlinear thermal coefficients is obtained. Two related cases are considered, one of them has a temperature condition on the fixed face x = 0 and the other one has a flux condition of the type −q0/ √ t (q0 > 0). In the first case, the source function de...

We study a one-dimensional free boundary problem for a non-linear diffusion–convection equation whose diffusivity is heterogeneous in space as well as being non-linear. Under the Bäcklund transformation the problem is reduced to an associated free boundary problem. We prove the existence and uniqueness, local in time, of the solution by using the F...

We consider the one-phase unidimensional Stefan problem with a convective boundary condition at the fixed face, with a heat transfer coefficient (proportional to the Biot number) h>0h>0. We study the limit of the temperature θhθh and the free boundary shsh when h goes to zero, and we also obtain an order of convergence. The goal of this paper is to...

We prove the existence and uniqueness, local in time, of the solution of a one-phase Stefan problem for a non-classical heat equation for a semi-infinite material with a convective boundary condition at the fixed face x = 0. Here the heat source depends on the temperature at the fixed face x = 0 that provides a heating or cooling effect depending o...

We study a one-phase Stefan problem for a semi-infinite material with temperature-dependent thermal conductivity and a convective term with a convective boundary condition at the fixed face x=0. We obtain sufficient conditions for data in order to have a parametric representation of the solution of the similarity type for t≥t 0 >0 with t 0 an arbit...

We consider one-phase nonclassical unidimensional Stefan problems for a source function
which depends on the heat flux, or the temperature on the fixed face . In the first case, we assume a temperature boundary condition, and in the second case we assume a heat flux boundary condition or a convective boundary condition at the fixed face. Exact sol...

The mathematical analysis of a one-phase Lamé–Clapeyron–Stefan problem with nonlinear thermal coefficients following [G.A. Tirskii, Two exact solutions of Stefan’s nonlinear problem, Sov. Phys. Dokl. 4 (1959) 288–292] is obtained. Two related cases are considered; one of them has a temperature condition on the fixed face x=0 and the other one has a...

This paper deals with a theoretical mathematical analysis of freezing (desublimation) of moisture in a finite porous medium with a heat flux condition at x=0. An equivalence between this problem and a system of Volterra integral equations is found. The existence of a unique local solution in time for this problem is also obtained.

A two-phase Stefan problem with heat source terms of a general similarity type in both liquid and solid phases for a semi-infinite phase-change material is studied. We assume the initial temperature is a negative constant and we consider two different boundary conditions at the fixed face x=0, a constant temperature or a heat flux of the form (q0>0...

Existence and uniqueness, local in time, of the solution of a one-phase Stefan problem for a non-classical heat equation for
a semi-infinite material is obtained by using the Friedman-Rubinstein integral representation method through an equivalent
system of two Volterra integral equations. Moreover, an explicit solution of a similarity type is pres...

We prove the existence and uniqueness, local in time, of the solution of a one-phase Stefan problem for a non-classical heat equation for a semi-infinite material with a heat flux boundary condition at the fixed face x = 0. Here the heat source depends on the temperature at the fixed face x = 0. We use the Friedman-Rubinstein integral representatio...

We prove the existence and uniqueness, local in time, of a solution for a one-phase Stefan problem of a non-classical heat equation for a semi-infinite material with temperature boundary condition at the fixed face. We use the Friedman-Rubinstein integral representation method and the Banach contraction theorem in order to solve an equivalent syste...

We study a one-phase Lamé-Clapeyron-Stefan problem for a semi-infinite material with nonlinear thermal coefficients and a constant temperature condition on the fixed face x=0, following G. A. Tirskii [Sov. Phys., Dokl. 4, 288–292 (1959); translation from Dokl. Akad. Nauk SSSR 125, 293–296 (1959; Zbl 0114.30104)]. We prove sufficient conditions for...

A two-phase Stefan problem with heat source terms in both liquid and solid phases for a semi-infinite phase-change material is considered. The internal heat source functions are given by g j (x,t)=(-1) j+1 ρl texp(-(x 2a j t+d j ) 2 ) (j=1 solid phase; j=2 liquid phase), ρ is the mass density, l is the fusion latent heat by unit of mass, a j 2 is t...

We review some recent results concerning a heat conduction problem with particular nonlinear thermal coefficients in both solid and liquid phases for a semi-infinite material x>0, with phase change temperature T 1 , an initial temperature T 2 (>T 1 ) and a heat flux of the type q(t)=q 0 t, imposed on the fixed face x=0. We find necessary and/or suf...

Unknown thermal coefficients of a semi-infinite material of Storm’s type through a phase-change process with an overspecified condition on the fixed face are determined. We follow the ideas developed in C. Rogers (Int. J. Non-Linear Mech. 21 (1986) 249–256) and in Tarzia (Adv. Appl. Math. 3 (1982) 74–82; Int. J. Heat Mass Transfer 26 (1983) 1151–11...

In wet soils, zones of saturation naturally develop in the vicinity of impermeable strata, surface ponds and subterranean cavities. Hydrology must be then concerned with transient flow through coexisting unsaturated and saturated zones. The models of advancing saturated zones necessarily involve a nonlinear free boundary problem.A closed-form analy...

We determinate unknown thermal coefficients of a semi-infinite material with an overspecified condition on the fixed face following the ideas developed in C. Rogers (ZAMP, 39, 122–128 (1988)) and in D.A. Tarzia (Adv. Appl. Math, 3, 74–82 (1982)). We also obtain formulae for the unknown coefficients and, the necessary and sufficient condition for th...

We consider two free boundary problems (one-phase non-classical unidimensional Stefan problems) for a non classical source function F depends on the heat flux or the total heat flux on the fixed face 0 x = . An explicit solution of a similarity type is obtained in both cases and the behavior of the first explicit solution is studied with respect to...