On the two dimensional fast phase transition equation: well-posedness and long-time dynamics

Khanmamedov, Azer

doi:10.1007/s00526-021-02078-3

Cited by 2 publications

(1 citation statement)

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“…To establish the well-posedness of solutions and the existence of a global attractor, the authors of [22] critically used the Strichartz estimates for the homogeneous Schrödinger equation which, as mentioned in [22, remark 6.1], is not applicable in a bounded domain case. Recently, in [23], it was shown that quasi-strong solutions of the two dimensional hyperbolic Cahn-Hilliard equation, with the quartic nonlinearity of class C 2,1 loc (R), are uniformly bounded. It was also noted there that, using this fact and arguing as in [18,20], one can prove the existence of the global attractor for quasi-strong solutions.…”

Section: Introductionmentioning

confidence: 99%

Attractors for some models of the Cahn–Hilliard equation with the inertial term

Khanmamedov

2023

Nonlinearity

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In this work, we consider the initial boundary value problem for the modified version of the Cahn–Hilliard equation with the inertial term in two dimensional smooth bounded domain. Under the optimal regularity condition on the quartic nonlinearity, by using the splitting method, we prove the existence of the absorbing set for the weak solutions. Then, applying the energy method, we show that the semigroup generated by the weak solutions possesses a global attractor of the optimal regularity, and thereby we give a positive answer to the question raised in (Grasselli et al 2009 On the 2D Cahn–Hilliard equation with inertial term Commun. PDE 34 137–70).

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