Abstract
In this paper, we study the long time behavior of solution for the initial-boundary value problem of convective Cahn–Hilliard equation in a 2D case. We show that the equation has a global attractor in H^{4}(Omega ) when the initial value belongs to H^{1}(Omega ).
Highlights
1 Introduction The dynamic properties of diffusion equations ensure the stability of diffusion phenomena and provide the mathematical foundation for the study of diffusion dynamics
By using a mean value theorem for integrals, we obtain the existence of a time t0 ∈ (T∗, T∗ + 1) such that u t0 2 ≤ c5 holds uniformly, the proof is complete
Using a mean value theorem for integrals, we obtain the existence of a time t0 ∈ (T, T + 1) such that
Summary
The dynamic properties of diffusion equations ensure the stability of diffusion phenomena and provide the mathematical foundation for the study of diffusion dynamics. Using the same method as [13], we obtain the lemma on the existence of global weak solution to problem (1)–(3). Remark 1.4 In the previous papers [18, 20, 21], my cooperators and I studied the existence of global attractor for a 2D convective Cahn–Hilliard equation.
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