Attractors for the nonclassical diffusion equations of Kirchhoff type with critical nonlinearity on unbounded domain†. Issue 4 (2nd October 2019)

• Record Type: Journal Article
• Authors: Zhang, Fanghong; Bai, Lihong
• Is Part Of: Dynamical systems. Volume 34:Issue 4(2019)
• Page Start: 640
• Page End: 667
• Publication Date: 2019-10-02
• Subjects: Nonclassical diffusion equation of Kirchhoff type -- global attractor -- exponential attractors -- fractal dimension -- critical nonlinearity; 35Q35 -- 35B40 -- 35B41; Differentiable dynamical systems -- Periodicals; 515.35205
• DOI: 10.1080/14689367.2019.1590533
• Languages: English
• ISSNs: 1468-9367

Abstract

ABSTRACT: In this paper, we investigate the long-time behavior of the solutions for the following nonclassical diffusion equations of Kirchhoff type u t − Δ u t − M ( ∥ ∇ u ∥ 2 ) Δ u + f ( x, u ) = g ( x ) . First, we prove the well-posedness of solution for the nonclassical diffusion equations of Kirchhoff type with critical nonlinearity on R N, then the existence of global attractor A is established in the natural energy space H 1 ( R N ) . Finally, we obtain the existence of exponential attractors E in H 1 ( R N ), as a product, the global attractor A has finite fractal dimension.