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- Title
Well-posedness and long-time behaviour for a singular phase field system of conserved type.
- Authors
GILARDI, GIANNI; ROCCA, ELISABETTA
- Abstract
In this paper, we study the well-posedness of a singular non-linear partial differential equation system and the long-time behaviour of its solutions. Namely, an equation ruling the evolution of the absolute temperature θ of the system (recently introduced in Bonetti, E., Colli, P., Fabrizio, M. & Gilardi, G. (2006) Modelling and long-time behaviour for phase transitions with entropy balance and thermal memory conductivity. Discrete Contin. Dyn. Syst. Ser. B, 6, 1001–1026 (electronic) and Bonetti, E., Colli, P., Fabrizio, M. & Gilardi, G. (2007) Global solution to a singular integrodifferential system related to the entropy balance. Nonlinear Anal., 66, 1949–1979) is coupled with a generalization of the well-known Cahn–Hilliard equation for the order parameter χ. In particular, under suitable assumptions on the non-linearities involved, we prove that the elements of the ω-limit set (i.e. the cluster points) of the trajectories solve the steady-state system that is naturally associated to the evolution problem.
- Subjects
BESSEL functions; TRANSCENDENTAL functions; PHASE transitions; STOKES equations; BIHARMONIC equations
- Publication
IMA Journal of Applied Mathematics, 2007, Vol 72, Issue 4, p498
- ISSN
0272-4960
- Publication type
Article
- DOI
10.1093/imamat/hxm015