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FOURTH ORDER GEOMETRIC EVOLUTION EQUATIONS

Published online by Cambridge University Press:  18 November 2010

GLEN WHEELER*
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia (email: gw@gew75.com)
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Abstract

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Type
Abstracts of Australasian PhD Theses
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

References

[1]Baras, P., Duchon, J. and Robert, R., ‘Evolution d’une interface par diffusion de surface’, Comm. Partial Differential Equations 9(4) (1984), 313335.Google Scholar
[2]Cahn, J. W., Elliott, C. M. and Novick-Cohen, A., ‘The Cahn–Hilliard equation with a concentration dependent mobility: motion by minus the Laplacian of the mean curvature’, European J. Appl. Math. 7(3) (1996), 287301.CrossRefGoogle Scholar
[3]Cahn, J. W. and Taylor, J. E., ‘Surface motion by surface diffusion’, Acta Metall. Mater. 42(4) (1994), 10451063.Google Scholar
[4]Davì, F. and Gurtin, M. E., ‘On the motion of a phase interface by surface diffusion’, Z. Angew. Math. Phys. 41(6) (1990), 782811.CrossRefGoogle Scholar
[5]Elliott, C. M. and Garcke, H., ‘Existence results for diffusive surface motion laws’, Adv. Math. Sci. Appl. 7(1) (1997), 465488.Google Scholar
[6]Escher, J., Mayer, U. F. and Simonett, G., ‘The surface diffusion flow for immersed hypersurfaces’, SIAM J. Math. Anal. 29(6) (1998), 14191433.CrossRefGoogle Scholar
[7]Fife, P. C., ‘Models for phase separation and their mathematics’, Electron. J. Differential Equations 2000(48) (2000), 126.Google Scholar
[8]Ito, K., ‘The surface diffusion flow equation does not preserve the convexity’, RIMS Kôkyûroku Bessatsu 1105 (1999), 1021.Google Scholar
[9]Kuwert, E. and Schatzle, R., ‘The Willmore flow with small initial energy’, J. Differential Geom. 57(3) (2001), 409441.CrossRefGoogle Scholar
[10]Kuwert, E. and Schatzle, R., ‘Gradient flow for the Willmore functional’, Comm. Anal. Geom. 10(2) (2002), 307339.CrossRefGoogle Scholar
[11]Kuwert, E. and Schatzle, R., ‘Removability of point singularities of Willmore surfaces’, Ann. of Math. (2) 160 (2004), 315357.CrossRefGoogle Scholar
[12]Mayer, U. F., ‘Numerical solutions for the surface diffusion flow in three space dimensions’, J. Comput. Appl. Math. 20(3) (2001), 361379.Google Scholar
[13]McCoy, J., ‘The surface area preserving mean curvature flow’, Asian J. Math. 7(1) (2003), 730.CrossRefGoogle Scholar
[14]McCoy, J., ‘The mixed volume preserving mean curvature flow’, Math. Z. 246(1–2) (2004), 155166.CrossRefGoogle Scholar
[15]McCoy, J., ‘Mixed volume preserving curvature flows’, Calc. Var. Partial Differential Equations 24(2) (2005), 131154.CrossRefGoogle Scholar
[16]Mullins, W. W., ‘Theory of thermal grooving’, J. Appl. Phys. 28 (1957), 333339.CrossRefGoogle Scholar
[17]Simonett, G., ‘The Willmore flow for near spheres’, Differential Integral Equations 14(8) (2001), 10051014.CrossRefGoogle Scholar
[18]Wheeler, G., ‘Lifespan theorem for simple constrained surface diffusion flows’. J. Math. Anal. Appl. (2010), to appear.Google Scholar
[19]Wheeler, G., McCoy, J. and Williams, G., ‘Lifespan theorem for constrained surface diffusion flows’. Math. Z. (2010), to appear.Google Scholar