Equations de Cahn-Hilliard généralisées dans un milieu déform able

✍ Scribed by Alain Miranville

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 418 KB
• Volume: 328
• Category: Article
• ISSN: 0764-4442
• DOI: 10.1016/s0764-4442(99)80331-0

✦ Synopsis

ProbPmes mathhmatiques de la m6caniquelMathematical Problems in Mechanics A bridged English Version We consider in this Note the coupling of generalized Cahn-Hilliard equations introduced by M. Gurtin in [6] with the Navier equation of linear elasticity. Note p&entt?e par Philippe G. CIARLET. 07644442/99/0328 IO95 0 AcadCmie des Sciences/Elsevier, Paris

We consider a first model (Equations (l)-( 8) below) for which we obtain the existence and uniqueness of weak solutions (Theo&me 1).

We then consider a simplified model in which we neglect the evolutive term in the Navier equation ( 2). In that case, we observe that the associated variational formulation can be uncoupled. This allows us to obtain the existence of the global attractor for the first component of the system. We finally prove, by constructing an exponential attractor, the finite dimensionality (in the sense of the fractal dimension) of the global attractor (Theoreme 2).

The details of the proofs, and also the study of more general situations, will appear in [9].