Moving-boundary and fixed-domain problems for a sixth-order thin-film equation

European Journal of Applied Mathematics

Volumn 15, Issue 6, 2004, Pages 713-754

  Flitton, J C ^a   King, J R ^a  

^a UNIVERSITY OF NOTTINGHAM   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 20444440804     PISSN: 09567925     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0956792504005753     Document Type: Article

References (21)

1. ARONSON, D. G. (1986) The porous medium equation. In: Some Problems in Nonlinear diffusion, Fasano, A. and Primicerio, M. (eds.), Lecture Notes in Maths 1224, Springer-Verlag.
2. BARRETT, J. W., LANGDON, S. & NUERNBERG, R. (2004) Finite element approximation of a sixth order nonlinear degenerate parabolic equation. Numer. Math. 96, 401-434.
3. BERNIS, F. & FRIEDMAN, A. (1990) Higher order nonlinear degenerate parabolic equations. J. Diff. Eq. 83, 179-206.
4. BERNIS, F., HULSHOF, J. & KING, J. R. (2000) Dipole and similarity solutions of the thin film equation in the half line. Nonlinearity, 13, 413-439.
5. BERTOZZI, A. L., BRENNER, M. P., DUPONT, T. F. & KADANOFF, L. P. (1994) Singularities and Similarities in Interface Flows. In: Trends and Perspectives in Applied Mathematics, Sirovich, L. (ed.). Springer-Verlag.
6. BOWEN, M. & KING, J. R. (2001) Asymptotic behaviour of the thin film equation in bounded domains. Euro. J. Appl. Math. 12, 135-157.
7. BOWEN, M., HULSHOF, J. & KING, J. R. (2001) Anomalous exponents and dipole solutions for the thin film equation. SIAM J. Appl. Math. 62, 149-179.
8. CONSTANTIN, P., DUPONT, T. F., GOLDSTEIN, R. E., KADANOFF, L. P., SHELLEY, M. J. & ZHOU, S.-M. (1993) Droplet breakup in a model of the Hele-Shaw cell. Phys. Rev. E, 47, 4169-4181.
9. DUPONT, T. F., GOLDSTEIN, R. E., KADANOFF, L. P. & ZHOU, S.-M. (1993) Finite-time singularity formation in Hele-Shaw systems. Phys. Rev. E, 47, 4182-4196.
10. EVANS, J. D., VYNNYCKY, M. & FERRO, S. P. (2000) Oxidation-induced stresses in the isolation oxidation of silicon. J. Eng. Math. 38, 191-218.
11. HOBART, K. D., KUB, F. J., FATEMI, M., TWIGG, M. E., THOMPSON, P. E., KUAN, T. S. & INOKI, C. K. (2000) Compliant substrates: A comparative study of the relaxation mechanisms of strained films bonded to high and low viscosity oxides. J. Electron. Mat. 29, 897-900.
12. HULSHOF, J. (2001) Some aspects of the thin film equation. Proc. Euro. Cong. Math. Vol. II. Prog. in Math. 202, 291-301. Birkhauser-Verlag.
13. HUANG, Z. & SUO, Z. (2002) Wrinkling of a compressed elastic film on a viscous layer. J Appl. Phys. 91, 1135-1142.
14. KING, J. R. (1986) Mathematical aspects of semiconductor process modelling. PhD thesis, University of Oxford.
15. KING, J. R. (1989) The isolation oxidation of silicon - the reaction-controlled case. SIAM J. Appl. Math. 49, 1064-1080.
16. KING, J. R. (2001) Two generalisations of the thin film equation. Math. Comp. Mod. 34, 737-756.
17. KING, J. R. & BOWEN, M. (2001) Moving boundary problems and non-uniqueness for the thin film equation. Euro. J. Appl. Math. 12, 321-356.
18. KOCH, M., HARRIS, N., MAAS, R., EVANS, A. G. R., WHITE, N. M. & BRUNNSCHWEILER, A. (1997) A novel micropump design with thick-film piezoelectric actuation Meas. Sci. Technol. 8, 49-57.
19. LANDAU, L. D. & LIFSHITZ, E. M. (1986) Theory of Elasticity, 3rd Ed. Pergamon Press.
20. SMITH, W. R., HOWISON, S. D. & MAYERS, D. F. (1996) Numerical and asymptotic solution of a sixth-order nonlinear diffusion equation and related coupled systems. IMA J. Appl. Math. 57, 79-98.
21. SMYTH, N. F. & HILL, J. M. (1988) High-order nonlinear diffusion. IMA J. Appl. Math. 40, 73-86.