Phase field approximation of a kinetic moving-boundary problem modelling dissolution and precipitation

Interfaces and Free Boundaries

Volumn 13, Issue 1, 2011, Pages 29-55

  Van Noorden, T L ^a   Eck, C ^b  

^a EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

^b UNIVERSITY OF STUTTGART   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79953138435     PISSN: 14639963     EISSN: None     Source Type: Journal    
DOI: 10.4171/IFB/247     Document Type: Article

References (17)

1. BERGH, J., & LÖFSTRÖM, J. Interpolation Spaces. An Introduction. Grundlehren Math. Wiss. 223, Springer, Berlin (1976). Zbl 0344.46071 MR 0482275
2. CAGINALP, G. An analysis of a phase field model of a free boundary. Arch. Ration. Mech. Anal. 92 (1986), 205-245. Zbl 0608.35080 MR 0816623
3. CAGINALP, G., & CHEN, X. Convergence of the phase field model to its sharp interface limits. Eur. J. Appl. Math. 9 (1998), 417-445. Zbl 0930.35024 MR 1643668
4. CAGINALP, G., CHEN, X., & ECK, C. A rapidly converging phase field model. Discrete Contin. Dynam. Systems 15 (2006), 1017-1034. Zbl 1119.80009 (Pubitemid 43935930)
5. CAGINALP, G., & FIFE, P. C. Dynamics of layered interfaces arising from phase boundaries. SIAM J. Appl. Math. 48 (1988), 506-518. MR 0941098
6. CAGINALP, G., & JONES, J. A derivation and analysis of phase field models of thermal alloys. Ann. Phys. 237 (1995), 66-107.
7. CAGINALP, G., & XIE, W. An analysis of phase-field alloys and transition layers. Arch. Ration. Mech. Anal. 142 (1998), 293-329. Zbl 0906.73008 MR 1645959 (Pubitemid 128373927)
8. DONEA, J., HUERTA, A., PONTHOT, J.-PH., & RODRÍGUEZ-FERRAN, A. Arbitrary Lagrangian-Eulerian methods. In: Encyclopedia of Computational Mechanics, Volume 1: Fundamentals, Chap. 14, E. Stein et al. (eds.), Wiley (2004).
9. ECK, C. Homogenization of a phase field model for binary mixtures. Multiscale Model. Simul. 3 (2004), 1-27. Zbl 1160.35332 MR 2123107 (Pubitemid 40555745)
10. FASANO, A. Mathematical models of some diffusive processes with free boundaries. MAT. Serie A: Conferencias, Seminarios y Trabajos de Mateḿatica 11, Universidad Austral, Facultad de Ciencias Empresariales (FCE-UA), Departamento de Mateḿatica, Rosario (2005). Zbl 1122.35001 MR 2285006
11. KNABNER, P., VAN DUIJN, C. J., & HENGST, S. An analysis of crystal dissolution fronts in flows through porous media. Part 1: Compatible boundary conditions. Adv. Water Res. 18 (1995), 171-185. (Pubitemid 26441794)
12. SOLONNIKOV, V. A. On boundary value problems for linear parabolic systems of differential equations of general form. Trudy Mat. Inst. Steklov. 83 (1965), 3-163 (in Russian);
13. English transl.: Proc. Steklov Inst. Math. 83 (1967), 1-184. Zbl 0164.12502 MR 0211083
14. VAN DUIJN, C. J., & POP, I. S. Crystal dissolution and precipitation in porous media: pore scale analysis. J. Reine Angew. Math. 577 (2004), 171-211. Zbl 1060.76116 MR 2108218 (Pubitemid 40031575)
15. VAN NOORDEN, T. L. Crystal precipitation and dissolution in a porous medium: Effective equations and numerical experiments. Multiscale Model. Simul. 7 (2009), 1220-1236. Zbl 1176.35020 MR 2480118
16. VAN NOORDEN, T. L. Crystal precipitation and dissolution in a thin strip. Eur. J. Appl. Math. 20 (2009), 69-91. Zbl 1154.82321 MR 2471668
17. VAN NOORDEN, T. L., & POP, I. S. A Stefan problem modelling crystal dissolution and precipitation. IMA J. Appl. Math. 73 (2008), 393-411. Zbl 1153.80004 MR 2411490 (Pubitemid 351523664)