Abstract
This article is devoted to the study of the long-time behavior of solutions of the following 4th order parabolic system in a bounded smooth domain $\Omega\subset\subset{\mathbb R}^n$: $$ b\partial_t u=-{\Delta_x} (a{\Delta_x} u-\alpha\partial_t u-f(u)+\tilde g )\,, \tag*{(1)} $$ where $u=(u^1,\cdots,u^k)$ is an unknown vector-valued function, $a$ and $b$ are given constant matrices such that $a+a^*>0$, $b=b^*>0$, $\alpha>0$ is a positive number, and $f$ and $g$ are given functions. Note that the nonlinearity $f$ is not assumed to be subordinated to the Laplacian. The existence of a finite dimensional global attractor for system (1) is proved under some natural assumptions on the nonlinear term $f$.
Citation
M. A. Efendiev. H. Gajewski. S. Zelik. "The finite dimensional attractor for a 4th order system of Cahn-Hilliard type with a supercritical nonlinearity." Adv. Differential Equations 7 (9) 1073 - 1100, 2002. https://doi.org/10.57262/ade/1367241460
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