A fourth-order parabolic equation with a logarithmic nonlinearity

Ahmed Bonfoh

doi:10.1017/s0004972700034249

A fourth-order parabolic equation with a logarithmic nonlinearity

Ahmed Bonfoh^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	35-48
Number of pages	14
Journal	Bulletin of the Australian Mathematical Society
Volume	69
Issue number	1
DOIs	https://doi.org/10.1017/s0004972700034249
State	Published - Feb 2004
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

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10.1017/s0004972700034249

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title = "A fourth-order parabolic equation with a logarithmic nonlinearity",

abstract = "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.",

author = "Ahmed Bonfoh",

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N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/1842592819

U2 - 10.1017/s0004972700034249

DO - 10.1017/s0004972700034249

M3 - Article

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EP - 48

JO - Bulletin of the Australian Mathematical Society

JF - Bulletin of the Australian Mathematical Society

IS - 1

ER -

A fourth-order parabolic equation with a logarithmic nonlinearity

Abstract

ASJC Scopus subject areas

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