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Mathematical modelling of a mushy region formation during sulphation of calcium carbonate
1. | Department of Mathematics, University of the Aegean, GR-832 00 Karlovassi, Samos, Greece |
References:
[1] |
G. Ali, V. Furuholt, R. Natalini and I. Torcicollo, A mathematical model of sulphite chemical aggression of limestones with high permeability. Part I. Modeling and qualitative analysis, Transport in Porous Media, 69 (2007), 109-122.
doi: 10.1007/s11242-006-9067-2. |
[2] |
G. Ali, V. Furuholt, R. Natalini and I. Torcicollo, A mathematical model of sulphite chemical aggression of limestones with high permeability. Part II: Numerical approximation, Transport in Porous Media, 69 (2007), 175-188.
doi: 10.1007/s11242-006-9068-1. |
[3] |
D. Aregba-Driollet, F. Diele and R. Natalini, A Mathematical Model for the SO2 Aggression to Calcium Carbonate Stones: Numerical Approximation and Asymptotic Analysis, SIAM J. APPL. MATH. , 64 (2004), 1636-1667.
doi: 10.1137/S003613990342829X. |
[4] |
F. Clareli, A. Fasano and R. Natalini, Mathematics and monument conservation: Free boundary models of marble sulfation, SIAM Journal on Applied Mathematics, 69 (2008), 149-168.
doi: 10.1137/070695125. |
[5] |
A. Fasano and R. Natalini, Lost Beauties of the Acropolis: What Mathematics Can Say, SIAM news, 2006. |
[6] |
T. Fatima, Multiscale Reaction Diffusion Systems Describing Concrete Corrosion: Modelling and Analysis, Ph.D thesis, Technical University of Eindhoven, 2013. |
[7] |
T. Fatima, N. Arab, E. P. Zemskov and A. Muntean, Homogenization of a reaction - diffusion system modeling sulfate corrosion of concrete in locally periodic perforated domains, Journal of Engineering Mathematics, 69 (2011), 261-276.
doi: 10.1007/s10665-010-9396-6. |
[8] |
T. Fatima and A. Muntean, Sulfate attack in sewer pipes: Derivation of a concrete corrosion model via two-scale convergence, Nonlinear Analysis: Real World Applications, 15 (2014), 326-344.
doi: 10.1016/j.nonrwa.2012.01.019. |
[9] |
T. Fatima, A. Muntean and T. Aiki, Distributed space scales in a semilinear reaction-diffusion system including a parabolic variational inequality: A well-posedness study, Adv. Math. Sci. Appl., 22 (2012), 295-318. |
[10] |
T. Fatima, A. Muntean and M. Ptashnyk, Unfolding-based corrector estimates for a reaction - diffusion system predicting concrete corrosion, Applicable Analysis, 91 (2012), 1129-1154.
doi: 10.1080/00036811.2011.625016. |
[11] |
F. R. Guarguaglini and R. Natalini, Fast reaction limit and large time behavior of solutions to a nonlinear model of sulphation phenomena, Commun. Partial Differ. Equations, 32 (2007), 163-189.
doi: 10.1080/03605300500361438. |
[12] |
F. R. Guarguaglini and R. Natalini, Global existence of solutions to a nonlinear model of sulphation phenomena in calcium carbonate stones, Nonlinear Analysis: Real World Applications, 6 (2005), 477-494.
doi: 10.1016/j.nonrwa.2004.09.007. |
[13] |
E. J. Hinch, Perturbation Methods, Cambridge University Press, 1991.
doi: 10.1017/CBO9781139172189. |
[14] |
A. A. Lacey and L. A. Herraiz, Macroscopic models for melting derived from averaging microscopic Stefan problems I: Simple geometries with kinetic undercooling or surface tension, Euro. Jnl. of Applied Mathematics, 11 (2002), 153-169.
doi: 10.1017/S0956792599004027. |
[15] |
A. A. Lacey and L. A. Herraiz, Macroscopic models for melting derived from averaging microscopic Stefan problems II: Effect of varying geometry and composition, Euro. Jnl. of Applied Mathematics, 13 (2002), 261-282.
doi: 10.1017/S0956792501004818. |
[16] |
R. J. Leveque, Finite Volume Methods for Hyperbolic Problems, Caimbridge University Press, 2002.
doi: 10.1017/CBO9780511791253. |
[17] |
C. V. Nikolopoulos, A mushy region in concrete corrosion, Applied Mathematical Modelling, 34 (2010), 4012-4030.
doi: 10.1016/j.apm.2010.04.005. |
[18] |
C. V. Nikolopoulos, Macroscopic models for a mushy region in concrete corrosion, Journal of Engineering Mathematics, 2014, DOI 10.1007/s10665-014-9743-0. |
[19] |
J. L. Schnoor, Enviromental Modeling, Fate and transport of pollutants in water, air, and soil, John Willey and Sons, Inc., 1996. |
show all references
References:
[1] |
G. Ali, V. Furuholt, R. Natalini and I. Torcicollo, A mathematical model of sulphite chemical aggression of limestones with high permeability. Part I. Modeling and qualitative analysis, Transport in Porous Media, 69 (2007), 109-122.
doi: 10.1007/s11242-006-9067-2. |
[2] |
G. Ali, V. Furuholt, R. Natalini and I. Torcicollo, A mathematical model of sulphite chemical aggression of limestones with high permeability. Part II: Numerical approximation, Transport in Porous Media, 69 (2007), 175-188.
doi: 10.1007/s11242-006-9068-1. |
[3] |
D. Aregba-Driollet, F. Diele and R. Natalini, A Mathematical Model for the SO2 Aggression to Calcium Carbonate Stones: Numerical Approximation and Asymptotic Analysis, SIAM J. APPL. MATH. , 64 (2004), 1636-1667.
doi: 10.1137/S003613990342829X. |
[4] |
F. Clareli, A. Fasano and R. Natalini, Mathematics and monument conservation: Free boundary models of marble sulfation, SIAM Journal on Applied Mathematics, 69 (2008), 149-168.
doi: 10.1137/070695125. |
[5] |
A. Fasano and R. Natalini, Lost Beauties of the Acropolis: What Mathematics Can Say, SIAM news, 2006. |
[6] |
T. Fatima, Multiscale Reaction Diffusion Systems Describing Concrete Corrosion: Modelling and Analysis, Ph.D thesis, Technical University of Eindhoven, 2013. |
[7] |
T. Fatima, N. Arab, E. P. Zemskov and A. Muntean, Homogenization of a reaction - diffusion system modeling sulfate corrosion of concrete in locally periodic perforated domains, Journal of Engineering Mathematics, 69 (2011), 261-276.
doi: 10.1007/s10665-010-9396-6. |
[8] |
T. Fatima and A. Muntean, Sulfate attack in sewer pipes: Derivation of a concrete corrosion model via two-scale convergence, Nonlinear Analysis: Real World Applications, 15 (2014), 326-344.
doi: 10.1016/j.nonrwa.2012.01.019. |
[9] |
T. Fatima, A. Muntean and T. Aiki, Distributed space scales in a semilinear reaction-diffusion system including a parabolic variational inequality: A well-posedness study, Adv. Math. Sci. Appl., 22 (2012), 295-318. |
[10] |
T. Fatima, A. Muntean and M. Ptashnyk, Unfolding-based corrector estimates for a reaction - diffusion system predicting concrete corrosion, Applicable Analysis, 91 (2012), 1129-1154.
doi: 10.1080/00036811.2011.625016. |
[11] |
F. R. Guarguaglini and R. Natalini, Fast reaction limit and large time behavior of solutions to a nonlinear model of sulphation phenomena, Commun. Partial Differ. Equations, 32 (2007), 163-189.
doi: 10.1080/03605300500361438. |
[12] |
F. R. Guarguaglini and R. Natalini, Global existence of solutions to a nonlinear model of sulphation phenomena in calcium carbonate stones, Nonlinear Analysis: Real World Applications, 6 (2005), 477-494.
doi: 10.1016/j.nonrwa.2004.09.007. |
[13] |
E. J. Hinch, Perturbation Methods, Cambridge University Press, 1991.
doi: 10.1017/CBO9781139172189. |
[14] |
A. A. Lacey and L. A. Herraiz, Macroscopic models for melting derived from averaging microscopic Stefan problems I: Simple geometries with kinetic undercooling or surface tension, Euro. Jnl. of Applied Mathematics, 11 (2002), 153-169.
doi: 10.1017/S0956792599004027. |
[15] |
A. A. Lacey and L. A. Herraiz, Macroscopic models for melting derived from averaging microscopic Stefan problems II: Effect of varying geometry and composition, Euro. Jnl. of Applied Mathematics, 13 (2002), 261-282.
doi: 10.1017/S0956792501004818. |
[16] |
R. J. Leveque, Finite Volume Methods for Hyperbolic Problems, Caimbridge University Press, 2002.
doi: 10.1017/CBO9780511791253. |
[17] |
C. V. Nikolopoulos, A mushy region in concrete corrosion, Applied Mathematical Modelling, 34 (2010), 4012-4030.
doi: 10.1016/j.apm.2010.04.005. |
[18] |
C. V. Nikolopoulos, Macroscopic models for a mushy region in concrete corrosion, Journal of Engineering Mathematics, 2014, DOI 10.1007/s10665-014-9743-0. |
[19] |
J. L. Schnoor, Enviromental Modeling, Fate and transport of pollutants in water, air, and soil, John Willey and Sons, Inc., 1996. |
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