Attractors for the nonclassical diffusion equations of Kirchhoff type with critical nonlinearity on unbounded domain†. Issue 4 (2nd October 2019) - Zhang, Fanghong; Bai, Lihong
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.