A. Araújo, S. Barbeiro, E. Cuesta, and A. Durán, Cross-Diffusion Systems for Image Processing: II. The Nonlinear Case, Journal of Mathematical Imaging and Vision, vol.58, issue.3, pp.427-446, 2017.

J. Berger, S. Gasparin, D. Dutykh, and N. Mendes, Accurate numerical simulation of moisture front in porous material, Building and Environment, vol.118, pp.211-224, 2004.
URL : https://hal.archives-ouvertes.fr/hal-01419018

J. Berger, S. Gasparin, D. Dutykh, and N. Mendes, On the Solution of Coupled Heat and Moisture Transport in Porous Material, Transport in Porous Media, vol.121, issue.3, pp.665-702, 2004.
URL : https://hal.archives-ouvertes.fr/hal-01770386

J. Berger, S. Guernouti, M. Woloszyn, and C. Buhe, Factors governing the development of moisture disorders for integration into building performance simulation, J. Building Eng, vol.3, issue.3, pp.1-15, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01819340

T. Chen, H. A. Levine, and P. E. Sacks, Analysis of a convective reaction-diffusion equation, Nonlinear Analysis: Theory, Methods & Applications, vol.12, issue.12, pp.1349-1370, 1988.

T. A. Driscoll, N. Hale, and L. N. Trefethen, , p.11, 2014.

L. C. Evans, Partial Differential Equations, vol.8, p.36, 2010.

L. Falchi, D. Slanzi, E. Balliana, G. Driussi, and E. Zendri, Rising damp in historical buildings: A Venetian perspective, Building and Environment, vol.131, pp.117-127, 2003.

S. Finsterle, Practical notes on local data-worth analysis, Water Resources Research, vol.51, issue.12, pp.9904-9924, 1925.

E. Franzoni, Rising damp removal from historical masonries: A still open challenge, Construction and Building Materials, vol.54, pp.123-136, 2003.

E. C. Gartland, On the Uniform Convergence of the Scharfetter-Gummel Discretization in One Dimension, SIAM J. Numer. Anal, vol.30, issue.3, pp.749-758, 1993.

L. Gosse, Viscous equations treated with L-splines and Steklov-Poincare operator in two dimensions, vol.4, p.11, 2017.

A. S. Guimarães, J. M. Delgado, and V. P. De-freitas, Mathematical analysis of the evaporative process of a new technological treatment of rising damp in historic buildings, Building and Environment, vol.45, issue.11, p.3, 2010.

M. Guizzardi, D. Derome, and J. Carmeliet, Water uptake in clay brick at different temperatures: Experiments and numerical simulations, Journal of Building Physics, vol.39, issue.4, p.34, 2016.

C. Hall and W. D. Hoff, Water Transport in Brick, Stone and Concrete, 2002.

P. Häupl, J. Grunewald, H. Fechner, and H. Stopp, Coupled heat air and moisture transfer in building structures, Int. J. Heat Mass Transf, vol.40, issue.7, pp.1633-1642, 1997.

A. Ho?a, Z. Matkowski, and J. Ho?a, Analysis of the Moisture Content of Masonry Walls in Historical Buildings Using the Basement of a Medieval Town Hall as an Example, Procedia Engineering, vol.172, issue.3, pp.363-368, 2017.

M. B. Janetti and P. Wagner, Analytical model for the moisture absorption in capillary active building materials, Building and Environment, vol.126, pp.98-106, 2003.

M. Karalashvili, W. Marquardt, and A. Mhamdi, Optimal experimental design for identification of transport coefficient models in convection-diffusion equations, Computers & Chemical Engineering, vol.80, pp.101-113, 1928.

M. Kumar-kumaran, International Energy Agency energy conservation in buildings and community systems programme Heat, air and moisture transfer through new and retrofitted insulated envelope parts

, Annex 24 Task 3/Final report: Material properties, p.22, 1996.

T. Kusano, On the first boundary problem for quasilinear systems of parabolic differential equations in non-cylindrical domains, Funkcialaj Ekvacioj, vol.7, issue.8, pp.103-118, 1965.

P. Lopez-arce, J. Garcia-guinea, D. Benavente, L. Tormo, and E. Doehne, Deterioration of dolostone by magnesium sulphate salt: An example of incompatible building materials at Bonaval Monastery, Spain. Construction and Building Materials, vol.23, issue.2, pp.846-855, 2009.

F. Ollivier and A. Sedoglavic, Algorithmes efficaces pour tester l'identifiabilité locale, Actes de la Conférence Internationale Francophone d'Automatique, p.25, 2002.

M. Peszynksa and S. Yi, Numerical methods for unsaturated flow with dynamic capillary pressure in heterogeneous porous media, Int. J. Numer. Anal. Model, vol.5, issue.3, pp.126-149, 2008.

J. R. Philip, D. A. De, and . Vries, Moisture movement in porous materials under temperature gradients, Transactions, vol.38, issue.2, pp.222-232, 1957.

E. Rirsch and Z. Zhang, Rising damp in masonry walls and the importance of mortar properties, Construction and Building Materials, vol.24, issue.10, p.3, 2010.

G. W. Scherer, Crystallization in pores, Cement and Concrete Research, vol.29, issue.8, pp.1347-1358, 1999.

G. W. Scherer, Stress from crystallization of salt, Cement and Concrete Research, vol.34, issue.9, pp.1613-1624, 2003.

L. F. Shampine and M. W. Reichelt, The MATLAB ODE Suite, SIAM J. Sci. Comput, vol.18, issue.9, pp.1-22, 1997.
URL : https://hal.archives-ouvertes.fr/hal-01333731

G. Söderlind and L. Wang, Adaptive time-stepping and computational stability, J. Comp. Appl. Math, vol.185, issue.2, p.11, 2006.

I. Torres and V. Peixoto-de-freitas, The influence of the thickness of the walls and their properties on the treatment of rising damp in historic buildings, Construction and Building Materials, vol.24, issue.8, p.3, 2010.

M. I. Torres and V. Peixoto-de-freitas, Treatment of rising damp in historical buildings: wall base ventilation, Building and Environment, vol.42, issue.1, pp.424-435, 2003.

D. Ucinski, Optimal Measurement Methods for Distributed Parameter System Identification, p.28, 2004.

E. Walter and Y. Lecourtier, Global approaches to identifiability testing for linear and nonlinear state space models, Math. Comp. Simul, vol.24, issue.6, pp.472-482, 1924.

E. Walter and L. Pronzato, Qualitative and quantitative experiment design for phenomenological models-A survey, Automatica, vol.26, issue.2, p.28, 1990.

A. Jumabekova, Ainagul.Jumabekova@univ-smb.fr URL

J. Berger, UMR 5271 CNRS, LOCIE, 73000 Chambéry, France E-mail address: Berger.Julien@univ-smb

D. Dutykh, , p.73000

F. Chambéry and L. , address: Denys.Dutykh@univ-smb.fr URL

H. and L. Meur, France E-mail address, Herve.LeMeur@math.u-psud.fr URL

M. Pailha,

. Ch and . Ménézo, UMR 5271 CNRS, LOCIE, 73000 Chambéry, France E-mail address: Christophe.Menezo@univ-smb