The Cahn-Hilliard/Allen-Cahn equation with inertial and proliferation terms

ŞEN Z., Khanmamedov A.

Journal of Mathematical Analysis and Applications, cilt.530, sa.2, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 530 Sayı: 2
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1016/j.jmaa.2023.127736
  • Dergi Adı: Journal of Mathematical Analysis and Applications
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, MathSciNet, zbMATH
  • Anahtar Kelimeler: Cahn-Hilliard equation, Global attractor, Hyperbolic relaxation
  • Hacettepe Üniversitesi Adresli: Evet

Özet

This paper is concerned with the initial-boundary value problem for the hyperbolic relaxation of the Cahn-Hilliard/Allen-Cahn equation with a proliferation term, in an arbitrary two dimensional smooth domain. With appropriate assumptions on the nonlinearities, we first prove the existence and uniqueness of an energy solution of the considered problem. Then, establishing the validity of the energy equality we show the regularity (in time) of the energy solution and its continuous dependence on the initial data. Under additional conditions on the nonlinearities, we also prove that the associated semigroup possesses a global attractor.