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Multi–component Cahn–Hilliard Systems with Singular Potentials: Theoretical Results.
- Source :
-
Applied Mathematics & Optimization . Dec2023, Vol. 88 Issue 3, p1-46. 46p. - Publication Year :
- 2023
-
Abstract
- We consider a system of nonlinear diffusion equations modelling (isothermal) phase segregation of an ideal mixture of N ≥ 2 components occupying a bounded region Ω ⊂ R d , d ≤ 3 . Our system is subject to a constant mobility matrix of coefficients, a free energy functional given in terms of singular entropy generated potentials and localized capillarity effects. We prove well-posedness and regularity results which generalize the ones obtained by Elliott and Luckhaus (IMA Preprint Ser 887, 1991). In particular, if d ≤ 2 , we derive the uniform strict separation of solutions from the singular points of the (entropy) nonlinearity. Then, even if d = 3 , we prove the existence of a global (regular) attractor as well as we establish the convergence of solutions to single equilibria. If d = 3 , this convergence requires the validity of the asymptotic strict separation property. This work constitutes the first part of an extended three-part study involving the phase behavior of multi-component systems, with a second part addressing the presence of nonlocal capillarity effects, and a final part concerning the numerical study of such systems along with some relevant application. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00954616
- Volume :
- 88
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Applied Mathematics & Optimization
- Publication Type :
- Academic Journal
- Accession number :
- 169995854
- Full Text :
- https://doi.org/10.1007/s00245-023-10048-8