1. Nacimiento: August 1979; continues uninterrupted to the present day.

2. The group has received subsidies from 1980 to the present through different institutions: CONICET (PIP, PID), ANPCyT (PICT, PAV, PICTO), SECyT, Prats Foundation, Antorchas Foundation, AFOSR-SOARD, National University of Rosario, Austral University.

3. Research Areas

 Dimension one

• Fixed, moving, and free boundary problems for the classical, non-classical, and fractional heat-diffusion differential equation.

Dimension two

• Elliptic and parabolic variational equations and inequalities.
• Optimal control problems of systems governed by partial differential equations.
• Numerical analysis of elliptic and parabolic differential equations.

4. Mathematical theories and elements that have been used in the work carried out

• Heat-Diffusion Equation: fundamental solution, jump formula.
• Volterra integral equations of the second kind.
• Functional analysis: distributions, Hilbert spaces, Banach and Sobolev spaces, fixed-point theorems.
• Elliptic and parabolic variational equations.
• Elliptic and parabolic variational inequalities.
• Calculation of variations, optimization.
• Optimal control theory of systems governed by PDEs.
• Quantitative finance: financial break-even point in an investment project, net present value.
• Numerical analysis of PDEs: finite element method, convergence and error estimates.
• Free boundary problems: phase change (Stefan), obstacle problem, Bingham fluid problem, diffusion-oxygen consumption problem, Tresca problem, Signorini problem.
• Soil science: root growth and nutrient uptake.
• Fractional differential equations: of Caputo, Riemann-Liouville type.

Applications

• Determination of thermal coefficients through phase change processes.
• Determination of nutrient uptake for crop root growth.
• Tumor localization.
• Solid-gas reaction-diffusion.
• Heat and mass transfer in high water content materials.
• Determining the financial break-even point in an investment project.

5. Group Formation

Director: Dr. Domingo A. Tarzia

Current members:

CONICET researchers:

1. Dr. Adriana C. BRIOZZO (CONICET – UA, Rosario). Adjunct Researcher and Full Professor;
2. Dr. Domingo A. TARZIA (CONICET – UA, Rosario). Senior Researcher and Full Professor;
3. Dr. Luis T. VILLA (CONICET – UNSa, Salta). Adjunct Researcher and Full Professor (in retirement);

4. Natalia N. SALVA (CONICET – UNCo – TEMADI (Bariloche Atomic Center)). Assistant Researcher;

University researchers with exclusive dedication:

1. Dr. Jorge BLENGINO ALBRIEU (Physics Dept., UNRC, Río Cuarto). JTP;
2. Dr. Claudia M. GARIBOLDI (Department of Mathematics, UNRC, Río Cuarto). Adjunct Professor;
3. Dr. Juan C. REGINATO (Department of Physics, UNRC, Río Cuarto). Associate Professor (in retirement);

University researchers with semi-exclusive dedication:

1. Dr. Ma. Fernanda NATALE (UA, Rosario). Full Professor;

CONICET Fellows:

1. Lic. Julieta BOLLATI (CONICET – UA, Rosario). Postgraduate Scholarship from 1/4/2014 to 31/3/2019 (Director: DA Tarzia; Co-director: AC Briozzo);
2. Dr. Andrea N. CERETANI (CONICET – UA, Rosario). Postdoctoral Fellowship from 1/4/2016 to 31/3/2018, (Director: DA Tarzia);
3. Dr. Sabrina D. ROSCANI (CONICET – UNR, Rosario). Postdoctoral Fellowship from 1/7/2016 to 30/6/2018, (Director: DA Tarzia);

Doctoral students with full-time dedication:

1. Mgt. Mariela OLGUIN (UNR, Rosario). Exclusive Adjunct Professor.

Former Argentine members in the past:

Cordoba: CV Turner.

Río Cuarto: M. Dzioba, A. Gonzalez, A. Rosso.

Rosario: LR Berrone, GG Garguichevich, PR Marangunic, EA Santillan Marcus, MC Sanziel, M. Stampella, C. Stoico, ED Tabacman.

6. Scientific journals in which members of the group have published work

1. A) Mathematics Journals:
   

• Annals of the National Academy of Exact, Physical and Natural Sciences of Buenos Aires (1997)
• Asymptotics Analysis (2007)
• Atti Physical and Mathematical Seminar at the University of Modena (1991)
• Bollettino dell'Unione Matematica Italiana (1982, 1983, 2003, 2006)
• Comptes Rendus de l'Academie des Sciences de Paris (1979)
• Demonstratio Mathematica (1999)
• MAT – Series A (2001, 2004, 2007, 2008, 2015)
• Mathematicae Notae (1979, 1980, 1981, 1982, 1983, 1989, 1990, 1991, 2006, 2007, 2008)
• Mathematics (2014)
• Proceedings of the American Mathematical Society (2001)
• Rendiconti Seminario Matematico dell'Università di Padova (1985)
• Rendiconti of the'Istituto di Matematica dell'Università di Trieste (2014)
• Journal of the Argentine Mathematical Union (1988, 1990, 1991, 1998, 2000)

1. B) Applied Mathematics Magazines:

• Advances in Applied Mathematics (1982)
• Advances in Mathematical Sciences and Applications (1994, 2014)
• Applicable Analysis (1989)
• Applied Mathematical Modeling (2015)
• Applied Mathematics (2015)
• Applied Mathematics Letters (1996)
• Applied Mathematics and Computation (2006, 2007, 2010)
• Communication on Pure and Applied Analysis (2010)
• Communications in Applied Analysis (2003)
• Computational and Applied Mathematics (1990, 1993, 2003)
• Fractional Calculus and Applied Analysis (2013, 2014)
• IMA Journal of Applied Mathematics (2002)
• Journal of Applied Analysis (2015)
• Journal of Applied Mathematics (2015)
• Journal of Mathematical Analysis and Applications (2007, 2011, 2012)
• Journal of Physics A: Mathematical and General (2000)
• Mathematical Methods in the Applied Sciences (2000, 2011)
• Nonlinear Analysis Series B: Real World Applications (2010, 2011)
• Nonlinear Analysis, Theory, Methods and Applications (1989, 2007)
• Quarterly of Applied Mathematics (1981, 1992, 1997, 2014)
• SIAM Journal on Applied Mathematics (2000)
• Zeitschrift fur Angewandte Mathematik und Mechanik (ZAMM) (1984)
• Zeitschrift fur Angewandte Mathematik und Physik (ZAMP) (2016)
• Mathematical Models and Methods in Applied Sciences (1999)

1. C) Journals of Differential Equations

• Boundary Value Problems (2011, 2015)
• Differential and Integral Equations (2014)
• Electronic Journal of Differential Equations (2006, 2007)
• International Journal of Differential Equations (2010, 2015)
• Journal of Differential Equations (1989)

1. D) Numerical Analysis Journals

• Numerical Methods for Partial Differential Equations (1999)
• International Journal of Numerical Methods for Calculation and Design in Engineering (1992)
• SIAM Journal on Numerical Analysis (1996)

1. E) Optimization and Control Journals

• Advances in Differential Equations and Control Processes (2008, 2014, 2016)
• Applied Mathematics and Optimization (2003)
• Computational Optimization and Applications (2012)
• Control and Cybernetics (2015)
• Journal of Control Theory and Applications (2013)
• Journal on Optimization, Theory and Applications (1990)

1. F) Journals of Physics, Mechanics and Engineering:

• Advances in Water Resources (1998)
• Advances in Renewable Energies and the Environment (2012)
• Engineering Analysis with Boundary Elements (ex Engineering Analysis) (1988)
• International Communications in Heat and Mass Transfer (1985, 1987, 1993, 1996, 1997, 1998, 1999, 2011)
• International Journal for Computational Methods in Engineering Science and Mechanics (2006)
• International Journal of Engineering Science (1989, 1990, 1993, 1996, 2000, 2003, 2016)
• International Journal of Heat and Mass Transfer (1983, 2008)
• International Journal of Non-Linear Mechanics (1999, 2012)
• International Journal of Non Newtonian Fluid Mechanics (2015)
• International Journal of Numerical Methods for Heat and Fluid Flow (2011)
• JP Journal of Heat and Mass Transfer (2007, 2008, 2011, 2016)
• Latin American Applied Research (Latin American Journal on Heat and Mass Transfer) (1984, 1985, 1991, 2011)
• Mathematical Problems in Engineering (2015)
• Meccanica (1989, 2001)
• PAMM – Proceedings on Applied Mathematics and Mechanics (2007)
• Thermal Science (2016)

1. G) Journals of Agronomy, Biology and Soil Science:

• Communications in Soil Science and Plant Analysis (2002)
• Journal of Biological Systems (2015)
• Journal of Plant Nutrition (2016)
• Plant and Soil (1993)
• Soil Science (1990, 1991, 2008)
• Soil Science Society of America Journal (2000)

1. H) Economics and Finance Journals:

• Journal of Economics and Financial Studies (2016)

7. Scientific journals of which members of the group have been and/or are members of the editorial committee:

• Mathematicae Notae (National Univ. of Rosario), 1986-2014.
• Notebooks of the “Beppo Levi” Institute of Mathematics (National University of Rosario), 1983-1996.
• Computational and Applied Mathematics (Springer), 1988-2006; 2009-.
• Journal of the Argentine Mathematical Union, 1996-.
• MAT -Series A: Lectures, Seminars and Papers on Mathematics (Austral University), 2000-.
• Economic Sciences Journal (National University of the Littoral), 2008-.
• Pioneer Journal of Mathematical Physics and its Applications, 2011-.
• Transnational Journal of Pure and Applied Mathematics, 2013-.
• Journal of the Faculty of Exact, Physical and Natural Sciences (National University of Córdoba), 2014-.

8. Scientific journals for which members of the group have acted as referees:

• Abstract and Applied Analysis
• African Diaspora Journal of Mathematics
• Annales Polinici Mathematics
• Applicable Analysis
• Applied Mathematical Modeling
• Applied Mathematics
• Applied Mathematics and Computation
• Arab Journal of Mathematical Sciences
• Boundary Value Problems
• British Journal of Mathematics and Computer Science
• Communications in Applied Analysis
• Computers and Mathematics with Applications
• Discrete and Continuous Dynamical Systems
• European Journal of Applied Mathematics
• Heat and Mass Transfer
• IET Control Theory and Applications
• Interfaces and Free Boundaries
• International Communications on Heat and Mass Transfer
• International Journal of Engineering Science
• International Journal of Engineering Science and Technology
• International Journal of Heat and Mass Transfer
• International Journal of Mathematics and Mathematical Sciences
• Journal of Applied Mathematics and Computing
• Journal of Differential Equations
• Journal of Porous Media
• Latin American Applied Research
• Latin American Journal of Heat and Mass Transfer
• Mathematical Methods in the Applied Sciences
• Physica D – Nonlinear Phenomena
• Numerical Heat Transfer
• Numerical Methods for Partial Differential Equations
• Quarterly of Applied Mathematics
• Journal of the Argentine Mathematical Union
• Technical Engineering Journal
• SIAM Journal on Applied Mathematics
• SIAM Journal on Control and Optimization
• SIAM Journal on Mathematical Analysis
• Springer Open

9. Members of the group are reviewers at: Mathematical Reviews (USA), Zentrablat Mathematik (Germany).

10. Scientific associations of which members of the group have been founding members:

• Argentine Association of Computational Mechanics (AMCA),
• Argentine Association of Applied, Computational and Industrial Mathematics (ASAMACI),
• Argentine Section of SIAM of the USA (AR-SIAM).

11. Residents abroad with whom members of the group have collaborated on projects:

• France: P. Souplet, H. Ghidouche, M. Boukrouche.
• Italy: Comparini, A. Farina, A. Fasano, L. Fusi, R. Gianni, P. Mannucci, M. Primicerio, R. Ricci, F. Rosso.
• Poland: Bobula, K. Twardowska.
• USA: L. Menaldi, M. Shillor.

12. Residents abroad with whom members of the group have had and/or have links for research purposes

• Germany: C. Meyer, Y. Luckho, F. Troelzsch.
• Bulgaria: Hristov.
• Brazil: R. Sampaio, G. Silva.
• Chile: C. Cortazar, M. Elgueta.
• Ecuador: M. Calahorrano, JC De Los Reyes.
• Spain: Casas, A. De Pablo, IJ Díaz, C. Vazquez, JL Vazquez.
• France: A. Damlamian, G. Duvaut, M. Fremond, M. Sofonea, L. Paoli.
• Italy: M. Amar, D. Andreucci, F. Falcini, R. Garra, F. Mainardi, E. Mascolo, D. Pallara, F. Talamucci, M. Ughi, V. Vespri.
• Poland: M. Migorski.
• USA: Alexiades, VR Voller, DG Wilson.

13. Books or monographs in research
14. DA TARZIA, “Introduction to elliptic variational inequalities and their applications to free boundary problems”, CLAMI-CONICET, No.5, Buenos Aires (1981), (206 pages).
15. DA TARZIA, “The two-phase Stefan problem and some related conduction problems”, Reuniöes em Matemática Aplicada e Computacao Cientifica, Vol. 5, Sociedade Brasileira de Matemática Aplicada e Computacional, Rio de Janeiro (1987), (137 pages).

• DA TARZIA, "A bibliography on moving-free boundary problems for the heat-diffusion equation. The Stefan problem", Progetto Nazionale MPI: Equazioni di Evoluzione e Applicazioni Fisico Matematiche", Firenze (1988) (with 2528 titles), (103 pages).

2. DA TARZIA, “Heat and mass transfer with phase change”, in “Heat and Mass Transfer. Fundamental Aspects”, 1st Postgraduate School in Heat and Mass Transfer ECAMAT'92, JC Ferreri (Ed.), CAMAT, Tandil (1992), Chapter 2, pp. 2.1-2.46 (46 pages). Enlarged version “Problems of heat conduction with phase change. The Stefan problem”, Posadas (1996), (52 pages).
3. DA TARZIA, "A bibliography on moving-free boundary problems for the heat-diffusion equation. The Stefan and related problems", MAT – Series A, Rosario, 2 (2000), pp 1-297 (with 5869 titles). ISSN: 1515-4904. It has been available online since November 13, 2000 at

http://web.austral.edu.ar/cienciasEmpresariales-investigacion-mat-A-02.asp   ó

http://www.austral.edu.ar/wp-content/uploads/2022/12/Tarzia-MAT-SerieA-22000.pdf

1. DA TARZIA, “Explicit and Approximated Solutions for Heat and Mass Transfer Problems with a Moving Interface”, Chapter 20, In Advanced Topics in Mass Transfer, Mohamed El-Amin (Ed.), InTech Open Access Publisher (626 pages), Rijeka (Croatia) (2011), pp. 439-484. ISBN: 978-953-307-333-0. Available in:

http://www.intechopen.com/articles/show/title/explicit-and-approximated-solutions-for-heat-and-mass-transfer-problems-with-a-moving-interface  (with 4000 downloads as of 5/12/2013):

The book containing the chapter can be accessed directly through the link:

http://www.intechopen.com/books/show/title/advanced-topics-in-mass-transfer

14. Scientific meetings organized by members of the group:
15. Seminar on the Stefan Problem and its Applications, Rosario, 04-08/07/1983;
16. Second Seminar on the Stefan Problem and its Applications, Rosario, 13-18/10/1986;

• III Seminar on Free Boundary Problems and their Applications, Rosario, 11-15/10/1988;

1. IV Seminar on Free Boundary Problems and their Applications, Rosario, 14-18/12/1992;
2. V Seminar on Free Boundary Problems and their Applications, Rosario, 19-21/12/1994;
3. VI Seminar on Free Boundary Problems and their Applications, Rosario, 16-18/12/1998;

• First Conference on Differential Equations, Numerical Analysis and Optimization, Rosario, 11-12/03/2004;
• VII School on Energy and Mass Transfer, Free Boundary Problems, and Applications, Rosario, 28/11 – 03/12/2005;

1. Workshop on Mathematical Modeling of Energy and Mass Transfer Processes, and Applications, Rosario, 05-07/12/2005;
2. Minisymposium IC/MP260/015 “Applied Mathematics in Latin America, Part I”, 6^th ICIAM 07, Zurich, 07/16-20/2007;
3. Minisymposium IC/MP262/015 “Applied Mathematics in Latin America, Part II”, 6^th ICIAM 07, Zurich, 07/16-20/2007;

• II Congress of Applied, Computational and Industrial Mathematics (II MACI 2009), Rosario, 14-16/12/2009.
• VII Italian-Latinamerican Conference on Applied and Industrial Mathematics (VII ITLA 2012), Rosario, 17-21/12/2012.

15. Publications of the proceedings of the organized scientific meetings:

• A. TARZIA (Ed.), “Seminar on the Stefan problem and its applications”, NOTEBOOKS of the “Beppo Levi” Institute of Mathematics, No. 11 (178 pages) and 12 (196 pages), Rosario (1984). ISSN: 03250690.
• A. TARZIA (Ed.), “II Seminar on the Stefan problem and its applications”, NOTEBOOKS of the “Beppo Levi” Institute of Mathematics, No. 13 (60 pages) and 14 (172 pages), Rosario (1987). ISSN: 03250690.
• A. TARZIA (Ed.), “III Seminar on free boundary problems and their applications”, Notebooks of the “Beppo Levi” Institute of Mathematics, No. 17 (152 pages) and 18 (100 pages), Rosario (1989). ISSN: 03250690.
• A. TARZIA (Ed.), “IV Seminar on free boundary problems and their applications”, Notebooks of the “Beppo Levi” Institute of Mathematics, No. 23 (129 pages) and 24 (130 pages), Rosario (1993). ISSN: 03250690.
• A. TARZIA (Ed.), “V Seminar on free boundary problems and their applications”, Notebooks of the “Beppo Levi” Institute of Mathematics, No. 25 (106 pages) and 26 (102 pages), Rosario (1995). ISSN: 03250690.
• A. TARZIA (Ed.), “VI Seminar on Free Boundary Problems and Their Applications”, MAT-Series A, # 3 (44 pages), # 4 (40 pages), # 5 (44 pages), Rosario (2001). ISSN: 1515-4904. Available at:

http://www.austral.edu.ar/wp-content/uploads/2022/12/TarziaEd-MAT-SerieA-32001.pdf

http://www.austral.edu.ar/wp-content/uploads/2022/12/TarziaEd-MAT-SerieA-42001.pdf

http://www.austral.edu.ar/wp-content/uploads/2022/12/TarziaEd-MAT-SerieA-52001.pdf

• A. TARZIA (Ed.), “First Conference on Differential Equations, Optimization and Numerical Analysis”, MAT – Series A, # 7 (42 pages), # 8 (27 pages), Rosario (2004). ISSN: 1515-4904. Available at:

http://www.austral.edu.ar/wp-content/uploads/2022/12/TarziaEd-MAT-SerieA-72005.pdf

http://www.austral.edu.ar/wp-content/uploads/2022/12/TarziaEd-MAT-SerieA-82005.pdf

• A. TARZIA – CV TURNER (Eds.), “Second Conference on Differential Equations, Optimization and Numerical Analysis”, MAT – Series A, # 10 (22 pages), Rosario (2005). ISSN: 1515-4904. Available at:

http://www.austral.edu.ar/wp-content/uploads/2022/12/Tarzia-TurnerEds-MAT-SerieA-102005.pdf

• C. MACIEL – DA TARZIA (Eds.), “Third Conference on Differential Equations, Optimization and Numerical Analysis”, MAT – Series A, # 14 (40 pages), Rosario (2007). ISSN: 1515-4904. Available at:

http://www.austral.edu.ar/wp-content/uploads/2022/12/Maciel-TarziaEds-MAT-SerieA-142007.pdf

• A. TARZIA – RH MASCHERONI (Eds.), “Workshop on Mathematical Modeling of Energy and Transfer Processes, and Applications”, MAT – Series A, # 15 (53 pages), Rosario (2008). ISSN: 1515-4904. Available at:

http://web.austral.edu.ar/descargas/facultad-cienciasEmpresariales/mat/Tarzia(Ed.)-MAT-SerieA-15(2008).pdf

• M. MANCINELLI – EA SANTILLAN MARCUS – DA TARZIA (Eds.), II Congress of Applied, Computational and Industrial Mathematics (II MACI 2009), ASAMACI, MACI, Vol. 2 (506 pages), Rosario (2009). Available at:

http://asamaci.org.ar/wp-content/uploads/2012/03/MACI-Vol-2-2009.pdf

• ACOSTA – J. ETCHEVERRY – F. REITICH – R. SPIES – D. TARZIA – C. TURNER – A. WILL (Eds.), “TAMI 2010 – Industrial Mathematics Workshop”, Courses and Seminars in Mathematics, Series B, Booklet 6 (57 pages), Department of Mathematics, Faculty of Exact and Natural Sciences, UBA, Buenos Aires (2010). Available at:

http://www.austral.edu.ar/wp-content/uploads/2022/12/CyS6.pdf

• A. TARZIA (Ed.), "VII Italian–Latin American Conference on Industrial and Applied Mathematics. Part 1", MAT – Series A, # 19 (42 pages), Rosario (2014). Available at:

http://www.austral.edu.ar/wp-content/uploads/2022/12/TarziaEd-MAT-SerieA-192014.pdf

• A. TARZIA (Ed.), "VII Italian–Latin American Conference on Industrial and Applied Mathematics. Part 2", MAT – Series A, # 20 (38 pages), Rosario (2015)

http://www.austral.edu.ar/wp-content/uploads/2022/12/TarziaEd-MAT-SerieA-202015.pdf