Well-Posedness and Global Attractors for Viscous Fractional Cahn-Hilliard Equations with Memory
FRACTAL AND FRACTIONAL, cilt.6, sa.9, 2022 (SCI-Expanded, SSCI, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 6 Sayı: 9
- Basım Tarihi: 2022
- Doi Numarası: 10.3390/fractalfract6090505
- Dergi Adı: FRACTAL AND FRACTIONAL
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Social Sciences Citation Index (SSCI), Scopus, INSPEC, Directory of Open Access Journals
- Anahtar Kelimeler: Cahn-Hilliard equation, fractional Laplacian, memory, PHASE-FIELD SYSTEM, ROBUST EXPONENTIAL ATTRACTORS, UNIFORM ATTRACTORS, LONGTIME BEHAVIOR, SINGULAR LIMIT, RELAXATION, DYNAMICS, MODEL
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Hacettepe Üniversitesi Adresli: Evet
Özet
We examine a viscous Cahn-Hilliard phase-separation model with memory and where the chemical potential possesses a nonlocal fractional Laplacian operator. The existence of global weak solutions is proven using a Galerkin approximation scheme. A continuous dependence estimate provides uniqueness of the weak solutions and also serves to define a precompact pseudometric. This, in addition to the existence of a bounded absorbing set, shows that the associated semigroup of solution operators admits a compact connected global attractor in the weak energy phase space. The minimal assumptions on the nonlinear potential allow for arbitrary polynomial growth.