-
Previous Article
A one dimensional free boundary problem for adsorption phenomena
- NHM Home
- This Issue
-
Next Article
Symmetry and positive definiteness of the tensor-valued spring constant derived from P1-FEM for the equations of linear elasticity
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. |
| [1] |
Jie Wang, Xiaoqiang Wang. New asymptotic analysis method for phase field models in moving boundary problem with surface tension. Discrete and Continuous Dynamical Systems - B, 2015, 20 (9) : 3185-3213. doi: 10.3934/dcdsb.2015.20.3185 |
| [2] |
Kersten Schmidt, Ralf Hiptmair. Asymptotic boundary element methods for thin conducting sheets. Discrete and Continuous Dynamical Systems - S, 2015, 8 (3) : 619-647. doi: 10.3934/dcdss.2015.8.619 |
| [3] |
Ziran Yin, Liwei Zhang. Perturbation analysis of a class of conic programming problems under Jacobian uniqueness conditions. Journal of Industrial and Management Optimization, 2019, 15 (3) : 1387-1397. doi: 10.3934/jimo.2018100 |
| [4] |
Fioralba Cakoni, Rainer Kress. Integral equations for inverse problems in corrosion detection from partial Cauchy data. Inverse Problems and Imaging, 2007, 1 (2) : 229-245. doi: 10.3934/ipi.2007.1.229 |
| [5] |
Fujun Zhou, Junde Wu, Shangbin Cui. Existence and asymptotic behavior of solutions to a moving boundary problem modeling the growth of multi-layer tumors. Communications on Pure and Applied Analysis, 2009, 8 (5) : 1669-1688. doi: 10.3934/cpaa.2009.8.1669 |
| [6] |
S. E. Pastukhova. Asymptotic analysis in elasticity problems on thin periodic structures. Networks and Heterogeneous Media, 2009, 4 (3) : 577-604. doi: 10.3934/nhm.2009.4.577 |
| [7] |
Joachim Escher, Anca-Voichita Matioc. Well-posedness and stability analysis for a moving boundary problem modelling the growth of nonnecrotic tumors. Discrete and Continuous Dynamical Systems - B, 2011, 15 (3) : 573-596. doi: 10.3934/dcdsb.2011.15.573 |
| [8] |
Giovanni Russo, Francis Filbet. Semilagrangian schemes applied to moving boundary problems for the BGK model of rarefied gas dynamics. Kinetic and Related Models, 2009, 2 (1) : 231-250. doi: 10.3934/krm.2009.2.231 |
| [9] |
Heting Zhang, Lei Li, Mingxin Wang. Free boundary problems for the local-nonlocal diffusive model with different moving parameters. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022085 |
| [10] |
Jesús Ildefonso Díaz. On the free boundary for quenching type parabolic problems via local energy methods. Communications on Pure and Applied Analysis, 2014, 13 (5) : 1799-1814. doi: 10.3934/cpaa.2014.13.1799 |
| [11] |
Jijun Liu, Gen Nakamura. Recovering the boundary corrosion from electrical potential distribution using partial boundary data. Inverse Problems and Imaging, 2017, 11 (3) : 521-538. doi: 10.3934/ipi.2017024 |
| [12] |
Navnit Jha. Nonpolynomial spline finite difference scheme for nonlinear singuiar boundary value problems with singular perturbation and its mechanization. Conference Publications, 2013, 2013 (special) : 355-363. doi: 10.3934/proc.2013.2013.355 |
| [13] |
Hua Chen, Shaohua Wu. The moving boundary problem in a chemotaxis model. Communications on Pure and Applied Analysis, 2012, 11 (2) : 735-746. doi: 10.3934/cpaa.2012.11.735 |
| [14] |
Timothy Blass, Rafael de la Llave. Perturbation and numerical methods for computing the minimal average energy. Networks and Heterogeneous Media, 2011, 6 (2) : 241-255. doi: 10.3934/nhm.2011.6.241 |
| [15] |
Nobuyuki Kato. Linearized stability and asymptotic properties for abstract boundary value functional evolution problems. Conference Publications, 1998, 1998 (Special) : 371-387. doi: 10.3934/proc.1998.1998.371 |
| [16] |
Xiao-Wen Chang, Ren-Cang Li. Multiplicative perturbation analysis for QR factorizations. Numerical Algebra, Control and Optimization, 2011, 1 (2) : 301-316. doi: 10.3934/naco.2011.1.301 |
| [17] |
P. Lima, L. Morgado. Analysis of singular boundary value problems for an Emden-Fowler equation. Communications on Pure and Applied Analysis, 2006, 5 (2) : 321-336. doi: 10.3934/cpaa.2006.5.321 |
| [18] |
Yuhong Dai, Ya-xiang Yuan. Analysis of monotone gradient methods. Journal of Industrial and Management Optimization, 2005, 1 (2) : 181-192. doi: 10.3934/jimo.2005.1.181 |
| [19] |
Sanming Liu, Zhijie Wang, Chongyang Liu. On convergence analysis of dual proximal-gradient methods with approximate gradient for a class of nonsmooth convex minimization problems. Journal of Industrial and Management Optimization, 2016, 12 (1) : 389-402. doi: 10.3934/jimo.2016.12.389 |
| [20] |
Abdon Atangana, Zakia Hammouch, Kolade M. Owolabi, Gisele Mephou. Preface: New trends on numerical analysis and analytical methods with their applications to real world problems. Discrete and Continuous Dynamical Systems - S, 2019, 12 (3) : i-i. doi: 10.3934/dcdss.201903i |
2020 Impact Factor: 1.213
Tools
Metrics
Other articles
by authors
[Back to Top]