Hostname: page-component-6dbcb7884d-lhnfz Total loading time: 0 Render date: 2025-02-14T01:54:00.405Z Has data issue: false hasContentIssue false
  • English
  • Français

On a system of nonlinear partial differential equations

Published online by Cambridge University Press:  17 April 2009

A. Sanih Bonfoh
A. Sanih Bonfoh
Affiliation:
University Kuala Lumpur, Malaysia France Institute, Sec 14, Jln, Teras Jernang, 43650 Bdr Baru Bangi, Selangor D.E., Malaysia
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We consider a generalised Cahn-Hilliard system with elasticity based on constitutives laws proposed by Gurtin, with a logarithmic free energy. We obtain some results on the existence and uniqueness of solutions.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 71 , Issue 3 , June 2005 , pp. 435 - 446
Copyright
Copyright © Australian Mathematical Society 2005

References

[1]Barrett, J.W. and Blowey, J.F., ‘An error bound for the finite element approximation of the Cahn-Hilliard equation with logarithmic free energy’, Numer. Math. 72 (1995), 1–20.CrossRefGoogle Scholar
[2]Bonfoh, A. and Miranville, A., ‘On Cahn-Hilliard-Gurtin equations’, Nonlinear Anal. 47 (2001), 3455–3466.CrossRefGoogle Scholar
[3]Cahn, J.W., ‘On spinodal decomposition’, Acta Metall. 9 (1961), 795–801.CrossRefGoogle Scholar
[4]Cahn, J.W. and Hilliard, J.E., ‘Free energy of a non-uniform system I. Interfacial free energy’, J. Chem. Phys. 2 (1958), 258–267.CrossRefGoogle Scholar
[5]Gurtin, M., ‘Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance’, Phys. D. 92 (1996), 178–192.CrossRefGoogle Scholar
[6]Lions, J.L., Quelques méthodes de résolutions des problèmes aux limites non linéaires (Dunod, Paris, 1969).Google Scholar
[7]Miranville, A., ‘Some generalizations of the Cahn-Hilliard equation’, Asymptotic Anal. 22 (2000), 235–259.Google Scholar
[8]Temam, R., Infinite dimensional dynamical systems in mechanics and physics, (2nd Edition) (Springer-Verlag, Berlin, Heidelberg, New York, 1997).CrossRefGoogle Scholar