A regularization of a reaction-diffusion system approximation to the two-phase Stefan problem

Nonlinear Analysis, Theory, Methods and Applications

Volumn 69, Issue 10, 2008, Pages 3512-3524

  Murakawa, Hideki ^a  

^a UNIVERSITY OF TOYAMA   (Japan)

Author keywords

Convergence rates; Free boundary; Reaction diffusion systems; Regularization; Stefan problem

Indexed keywords

COMPUTER NETWORKS; DIFFUSION; DIFFUSION IN LIQUIDS; POLYNOMIAL APPROXIMATION; SEMICONDUCTOR DOPING; TWO PHASE FLOW;

CONVERGENCE RATES; FREE BOUNDARY; REACTION-DIFFUSION SYSTEMS; REGULARIZATION; STEFAN PROBLEM;

REACTION RATES;

EID: 51349134540     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2007.09.038     Document Type: Article

References (16)

1. Beckett G., Mackenzie J.A., and Robertson M.L. A moving mesh finite element method for the solution of two-dimensional Stefan problems. J. Comput. Phys. 168 (2001) 500-518
2. Crank J. Free and Moving Boundary Problems (1984), Clarendon Press, Oxford
3. Crooks E.C.M., Dancer E.N., Hilhorst D., Mimura M., and Ninomiya H. Spatial segregation limit of a competition-diffusion system with Dirichlet boundary conditions. Nonlinear Anal. Real World Appl. 5 (2004) 645-665
4. Dancer E.N., Hilhorst D., Mimura M., and Peletier L.A. Spatial segregation limit of a competition-diffusion system. European J. Appl. Math. 10 (1999) 97-115 533-557
5. Friedman A. The Stefan problem in several space variables. Trans. Amer. Math. Soc. 133 (1968) 51-87
6. Grossmann C., and Noack A. Smoothing and Rothe's method for Stefan problems in enthalpy form. J. Comput. Appl. Math. 138 (2002) 347-366
7. Hilhorst D., Iida M., Mimura M., and Ninomiya H. A competition-diffusion system approximation to the classical two-phase Stefan problem. Jpn. J. Ind. Appl. Math. 18 (2001) 161-180
8. Hilhorst D., Iida M., Mimura M., and Ninomiya H. A reaction-diffusion system approximation to the classical two-phase Stefan problem. Nonlinear Anal. Real World Appl. 47 (2001) 801-812
9. Hilhorst D., Mimura M., and Schätzle R. Vanishing latent heat limit in a Stefan-like problem arising in biology. Nonlinear Anal. 4 (2003) 261-285
10. Ladyženskaja O.A., Solonnikov V.A., and Ural'ceva N.N. Linear and quasilinear equations of parabolic type. Trans. Math. Monographs vol. 23 (1968), American Mathematical Society, Providence, RI
11. Lunardi A. Analytic semigroups and regularity in parabolic problems. Progress in Nonlinear Differential Equations and their Applications vol. 16 (1995), Birkhäuser, Basel, Boston, Berlin
12. Meirmanov A.M. The Stefan Problem (1992), Walter de Gruyter, Berlin
13. Murakawa H. Reaction-diffusion system approximation to degenerate parabolic systems. Nonlinearity 20 (2007) 2319-2332
14. Nochetto R.H. Error estimates for two-phase Stefan problems in several space variables, I: Linear boundary conditions. Calcolo 22 (1985) 457-499
15. Nochetto R.H. A note on the approximation of free boundaries by finite element methods. RAIRO Modél. Math. Anal. Num. 20 (1986) 355-368
16. Nochetto R.H. A class of non-degenerate two-phase Stefan problems in several space variables. Comm. Partial Differential Equations 12 (1987) 111-138