Long-time dynamics of the 2D nonisothermal hyperbolic Cahn-Hilliard equations

YAYLA S.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, cilt.45, ss.5513-5544, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 45
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1002/mma.8124
  • Dergi Adı: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.5513-5544
  • Anahtar Kelimeler: Cahn-Hilliard equation, convergence to stationary point, enthalpy, Fourier law, global attractor, hyperbolic relaxation, Maxwell-Cattaneo law, ROBUST EXPONENTIAL ATTRACTORS, GLOBAL ATTRACTORS, SINGULAR PERTURBATIONS, ASYMPTOTIC-BEHAVIOR, EQUILIBRIA, SYSTEM, CONVERGENCE, GROWTH, MODEL
  • Hacettepe Üniversitesi Adresli: Evet

Özet

In this paper, we consider the hyperbolic relaxation of the nonisothermal Cahn-Hilliard equation based on either Fourier law or Maxwell-Cattaneo law for heat conduction. In the Maxwell-Cattaneo case, we reformulate the problem by using enthalpy instead of relative temperature. In both cases, we prove the existence of the global attractor for the weak solutions of the problem. Moreover, for both laws, we establish that every full trajectory in the global attractor converges to a single stationary point as t -> infinity and another single stationary point as t -> -infinity. Consequently, we infer that the global attractor is equal to a union of the unstable manifolds emanating from the stationary points.