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A fourth-order parabolic equation with a logarithmic nonlinearlity

Published online by Cambridge University Press:  17 April 2009

Ahmed Bonfoh
Ahmed Bonfoh
Affiliation:
University Kuala Lumpur, Malaysia France Institute, Sec. 14, Jln Teras Jernang, 43650 Bdr Baru Bangi, Selangor D.E., Malaysia
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We consider some generalisations of the Cahn—Hilliard equation based on constitutive equations derived by M. Gurtin in (1996) with a logarithmic free energy. Compared to the classical Cahn—Hilliard equation (see [4, 5]), these models take into account the work of internal microforces and the anisotropy of the material. We obtain the existence and uniqueness of solutions results and then prove the existence of finite dimensional attractors.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 69 , Issue 1 , February 2004 , pp. 35 - 48
Copyright
Copyright © Australian Mathematical Society 2004

References

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