Adriana Briozzo - Academia.edu (original) (raw)
Papers by Adriana Briozzo
Nonlinear Analysis-real World Applications, Oct 1, 2022
International series of numerical mathematics, 2006
ABSTRACT Existence and uniqueness, local in time, of the solution of a one-phase Stefan problem f... more ABSTRACT 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 presented for a non-classical heat source depending on time and heat flux on the fixed face x = 0.
Nonlinear Analysis-real World Applications, Oct 1, 2019
A non-classical one dimensional Stefan problem with thermal coefficients temperature dependent an... more 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 free boundary with respect to latent heat fusion is studied. The analysis of several particular cases are given.
Journal of Mathematical Analysis and Applications, May 1, 2012
We consider the one-phase unidimensional Stefan problem with a convective boundary condition at t... more 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 > 0. We study the limit of the temperature θ h and the free boundary s h when h goes to zero, and we also obtain an order of convergence. The goal of this paper is to do the mathematical analysis of the physical behavior given in [C. Naaktgeboren, The zero-phase Stefan problem, Int. J. Heat Mass Transfer 50 (2007) 4614-4622].
International Journal of Non-linear Mechanics, Sep 1, 2021
Different one-phase Stefan problems for a semi-infinite slab are considered, involving a moving p... more 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 radiativeconvective boundary condition at the fixed face. The velocity that arises in the convective term of the diffusion-convection equation is assumed to depend on temperature and time. In each case, an equivalent ordinary differential problem is obtained giving rise to a system of an integral equation coupled with a condition for the parameter that characterizes the free boundary, which is solved though a double-fixed point analysis. Some solutions for particular thermal coefficients are provided.
A one-phase unidimensional Stefan problem with a convective boundary condition at the fixed face ... more A one-phase unidimensional Stefan problem with a convective boundary condition at the fixed face x = 0, with a heat transfer coefficient h > 0 (proportional to the Biot number) and an initial position of the free boundary b = s(0) > 0 is considered. We study the limit of the temperature θ = θ b,h and the free boundary s = s b,h when b → 0 + (for all h > 0) and we also obtain an order of convergence. Moreover, we study the limit of the temperature θ b,h and the free boundary s b,h when (b, h) → (0 + , 0 +).
Differential and Integral Equations, Nov 1, 2014
The mathematical analysis of two one-phase unidimensional and non-classical Stefan problems with ... more The mathematical analysis of two one-phase unidimensional and non-classical Stefan problems with nonlinear thermal coecients 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= p t (q0 > 0) : In the first case, the source function depends on the heat flux at the fixed face x = 0; and in the other case it depends on the temperature at the fixed face x = 0: In both cases, we obtain sufficient conditions in order to have the existence of an explicit solution of a similarity type, which is given by using a double fixed point.Fil: Briozzo, Adriana Clotilde. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Austral. Facultad de Cs.empresariales. Departamento de Matemáticas; ArgentinaFil: Natale, María Fernanda. Universidad Austral. Facultad de Cs.empresariales. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin
Zeitschrift für Angewandte Mathematik und Physik, Mar 21, 2017
We study the supercooled one-phase Stefan problem for a semi-infinite material with temperature-d... more We study the supercooled one-phase Stefan problem for a semi-infinite material with temperature-dependent thermal conductivity at the fixed face x = 0. We obtain sufficient conditions for data in order to have existence of a solution of similarity type, local in time and finite-time blow-up occurs. This explicit solution is obtained through the unique solution of an integral equation with the time as a parameter.
International Journal of Non-linear Mechanics, Mar 1, 1999
We consider a nonlinear one-dimensional Stefan problem for a semi-infinite material x > 0, with p... more 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 thermal coefficients are determined for the free boundary problem and for the associate moving boundary problem and we give sufficient conditions to obtain a parametric representation of a similarity type solution. Moreover, we give formulae for the thermal coefficients in both cases.
Journal of Applied Analysis, Nov 4, 2015
We study a one-phase Stefan problem for a semi-infinite material with temperature-dependent therm... 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 x = 0. We obtain sufficient conditions for data in order to have a parametric representation of the solution of similarity type for t ≥ t 0 > 0 with t 0 an arbitrary positive time. This explicit solution is obtained through the unique solution of an integral equation with the time as a parameter.
Nonlinear Analysis-theory Methods & Applications, Sep 1, 2007
This paper deals with a theoretical mathematical analysis of freezing (desublimation) of moisture... more 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.
Mathematics, Dec 27, 2013
We consider two one-phase nonlinear one-dimensional Stefan problems for a semi-infinite material ... more 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) = q 0 √ t , and in the second case, we assume a temperature boundary condition T = T s < T f at the fixed face. Solutions of similarity type are obtained in both cases, and the equivalence of the two problems is demonstrated. We also give procedures in order to compute the explicit solution.
International Journal of Non-linear Mechanics, Apr 1, 2023
Zeitschrift für Angewandte Mathematik und Physik, Apr 30, 2021
A one-dimensional Stefan problem with spherical symmetry corresponding to the evaporation process... more 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.
Computational & Applied Mathematics, Feb 3, 2018
We consider a nonlinear one-dimensional Stefan problem for a semi-infinite material x > 0, with p... more 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 thermal coefficients are determined for the free boundary problem and for the associate moving boundary problem and we give sufficient conditions to obtain a parametric representation of a similarity type solution. Moreover, we give formulae for the thermal coefficients in both cases.
Zeitschrift für Angewandte Mathematik und Physik, Apr 1, 2016
We consider a nonlinear one-dimensional Stefan problem for a semi-infinite material x > 0, with p... more 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 and we assume a convective boundary condition at the fixed face x = 0. An unique explicit solution of similarity type is obtained. Moreover, asymptotic behavior of the solution when h → +∞ is studied.
Acta Mechanica, Oct 20, 2019
Mathematical Methods in The Applied Sciences, Jan 10, 2020
We consider a two-phase Stefan problem for a semi-infinite body x > 0, with a convective boundary... more 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 solution to this problem converges to the solution to the analogous one with a temperature boundary condition when the heat transfer coefficient h → +∞. Moreover, we analyze the dependence of the free boundary respecting to the jump density. KEYWORDS two-phase Stefan problem, density jump, asymptotic behavior, phase-change process MSC CLASSIFICATION 35R35; 80A22; 35C05 1 (s(t), t) = 2 (s(t), t) = 0 , t > 0 , (3)
International Communications in Heat and Mass Transfer, Oct 1, 1997
We consider a nonlinear one-dimensional Stefan problem for a semi-infinite material x > 0, with p... more 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 thermal coefficients are determined for the free boundary problem and for the associate moving boundary problem and we give sufficient conditions to obtain a parametric representation of a similarity type solution. Moreover, we give formulae for the thermal coefficients in both cases.
MAT., Oct 1, 2004
A two-phase Stefan problem with heat source terms in both liquid and solid phases for a semi-in¯n... more A two-phase Stefan problem with heat source terms in both liquid and solid phases for a semi-in¯nite phase-change material is considered. The internal heat source functions are given by g j (x; t) = (¡1) j+1 ½l t exp ³ ¡(x 2a j p t + d j) 2´(j = 1 solid phase; j = 2 liquid phase), ½ is the mass density, l is the fusion latent heat by unit of mass; a 2 j is the di®usion coe±cient, x is spatial variable, t is the temporal variable and d j 2 R. A similarity solution is obtained for any data when a temperature boundary condition is imposed at the¯xed face x = 0; when a°ux condition of the type ¡q 0 = p t (q 0 > 0) is imposed on x = 0 then there exists a similarity solution if and only if a restriction on q 0 is satis¯ed.
Nonlinear Analysis-real World Applications, Oct 1, 2022
International series of numerical mathematics, 2006
ABSTRACT Existence and uniqueness, local in time, of the solution of a one-phase Stefan problem f... more ABSTRACT 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 presented for a non-classical heat source depending on time and heat flux on the fixed face x = 0.
Nonlinear Analysis-real World Applications, Oct 1, 2019
A non-classical one dimensional Stefan problem with thermal coefficients temperature dependent an... more 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 free boundary with respect to latent heat fusion is studied. The analysis of several particular cases are given.
Journal of Mathematical Analysis and Applications, May 1, 2012
We consider the one-phase unidimensional Stefan problem with a convective boundary condition at t... more 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 > 0. We study the limit of the temperature θ h and the free boundary s h when h goes to zero, and we also obtain an order of convergence. The goal of this paper is to do the mathematical analysis of the physical behavior given in [C. Naaktgeboren, The zero-phase Stefan problem, Int. J. Heat Mass Transfer 50 (2007) 4614-4622].
International Journal of Non-linear Mechanics, Sep 1, 2021
Different one-phase Stefan problems for a semi-infinite slab are considered, involving a moving p... more 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 radiativeconvective boundary condition at the fixed face. The velocity that arises in the convective term of the diffusion-convection equation is assumed to depend on temperature and time. In each case, an equivalent ordinary differential problem is obtained giving rise to a system of an integral equation coupled with a condition for the parameter that characterizes the free boundary, which is solved though a double-fixed point analysis. Some solutions for particular thermal coefficients are provided.
A one-phase unidimensional Stefan problem with a convective boundary condition at the fixed face ... more A one-phase unidimensional Stefan problem with a convective boundary condition at the fixed face x = 0, with a heat transfer coefficient h > 0 (proportional to the Biot number) and an initial position of the free boundary b = s(0) > 0 is considered. We study the limit of the temperature θ = θ b,h and the free boundary s = s b,h when b → 0 + (for all h > 0) and we also obtain an order of convergence. Moreover, we study the limit of the temperature θ b,h and the free boundary s b,h when (b, h) → (0 + , 0 +).
Differential and Integral Equations, Nov 1, 2014
The mathematical analysis of two one-phase unidimensional and non-classical Stefan problems with ... more The mathematical analysis of two one-phase unidimensional and non-classical Stefan problems with nonlinear thermal coecients 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= p t (q0 > 0) : In the first case, the source function depends on the heat flux at the fixed face x = 0; and in the other case it depends on the temperature at the fixed face x = 0: In both cases, we obtain sufficient conditions in order to have the existence of an explicit solution of a similarity type, which is given by using a double fixed point.Fil: Briozzo, Adriana Clotilde. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Austral. Facultad de Cs.empresariales. Departamento de Matemáticas; ArgentinaFil: Natale, María Fernanda. Universidad Austral. Facultad de Cs.empresariales. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin
Zeitschrift für Angewandte Mathematik und Physik, Mar 21, 2017
We study the supercooled one-phase Stefan problem for a semi-infinite material with temperature-d... more We study the supercooled one-phase Stefan problem for a semi-infinite material with temperature-dependent thermal conductivity at the fixed face x = 0. We obtain sufficient conditions for data in order to have existence of a solution of similarity type, local in time and finite-time blow-up occurs. This explicit solution is obtained through the unique solution of an integral equation with the time as a parameter.
International Journal of Non-linear Mechanics, Mar 1, 1999
We consider a nonlinear one-dimensional Stefan problem for a semi-infinite material x > 0, with p... more 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 thermal coefficients are determined for the free boundary problem and for the associate moving boundary problem and we give sufficient conditions to obtain a parametric representation of a similarity type solution. Moreover, we give formulae for the thermal coefficients in both cases.
Journal of Applied Analysis, Nov 4, 2015
We study a one-phase Stefan problem for a semi-infinite material with temperature-dependent therm... 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 x = 0. We obtain sufficient conditions for data in order to have a parametric representation of the solution of similarity type for t ≥ t 0 > 0 with t 0 an arbitrary positive time. This explicit solution is obtained through the unique solution of an integral equation with the time as a parameter.
Nonlinear Analysis-theory Methods & Applications, Sep 1, 2007
This paper deals with a theoretical mathematical analysis of freezing (desublimation) of moisture... more 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.
Mathematics, Dec 27, 2013
We consider two one-phase nonlinear one-dimensional Stefan problems for a semi-infinite material ... more 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) = q 0 √ t , and in the second case, we assume a temperature boundary condition T = T s < T f at the fixed face. Solutions of similarity type are obtained in both cases, and the equivalence of the two problems is demonstrated. We also give procedures in order to compute the explicit solution.
International Journal of Non-linear Mechanics, Apr 1, 2023
Zeitschrift für Angewandte Mathematik und Physik, Apr 30, 2021
A one-dimensional Stefan problem with spherical symmetry corresponding to the evaporation process... more 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.
Computational & Applied Mathematics, Feb 3, 2018
We consider a nonlinear one-dimensional Stefan problem for a semi-infinite material x > 0, with p... more 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 thermal coefficients are determined for the free boundary problem and for the associate moving boundary problem and we give sufficient conditions to obtain a parametric representation of a similarity type solution. Moreover, we give formulae for the thermal coefficients in both cases.
Zeitschrift für Angewandte Mathematik und Physik, Apr 1, 2016
We consider a nonlinear one-dimensional Stefan problem for a semi-infinite material x > 0, with p... more 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 and we assume a convective boundary condition at the fixed face x = 0. An unique explicit solution of similarity type is obtained. Moreover, asymptotic behavior of the solution when h → +∞ is studied.
Acta Mechanica, Oct 20, 2019
Mathematical Methods in The Applied Sciences, Jan 10, 2020
We consider a two-phase Stefan problem for a semi-infinite body x > 0, with a convective boundary... more 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 solution to this problem converges to the solution to the analogous one with a temperature boundary condition when the heat transfer coefficient h → +∞. Moreover, we analyze the dependence of the free boundary respecting to the jump density. KEYWORDS two-phase Stefan problem, density jump, asymptotic behavior, phase-change process MSC CLASSIFICATION 35R35; 80A22; 35C05 1 (s(t), t) = 2 (s(t), t) = 0 , t > 0 , (3)
International Communications in Heat and Mass Transfer, Oct 1, 1997
We consider a nonlinear one-dimensional Stefan problem for a semi-infinite material x > 0, with p... more 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 thermal coefficients are determined for the free boundary problem and for the associate moving boundary problem and we give sufficient conditions to obtain a parametric representation of a similarity type solution. Moreover, we give formulae for the thermal coefficients in both cases.
MAT., Oct 1, 2004
A two-phase Stefan problem with heat source terms in both liquid and solid phases for a semi-in¯n... more A two-phase Stefan problem with heat source terms in both liquid and solid phases for a semi-in¯nite phase-change material is considered. The internal heat source functions are given by g j (x; t) = (¡1) j+1 ½l t exp ³ ¡(x 2a j p t + d j) 2´(j = 1 solid phase; j = 2 liquid phase), ½ is the mass density, l is the fusion latent heat by unit of mass; a 2 j is the di®usion coe±cient, x is spatial variable, t is the temporal variable and d j 2 R. A similarity solution is obtained for any data when a temperature boundary condition is imposed at the¯xed face x = 0; when a°ux condition of the type ¡q 0 = p t (q 0 > 0) is imposed on x = 0 then there exists a similarity solution if and only if a restriction on q 0 is satis¯ed.