Finite fractal dimension of pullback attractors for a nonclassical diffusion equation

Abstract

In this paper, we investigate the finite fractal dimension of pullback attractors for a nonclassical diffusion equation in $ H^1_0(\Omega) $. First, we prove the existence of pullback attractors for a nonclassical diffusion equation with arbitrary polynomial growth condition by applying the operator decomposition method. Then, by the fractal dimension theorem of pullback attractors given by [6], we prove the finite fractal dimension of pullback attractors for a nonclassical diffusion equation in $ H^1_0(\Omega) $.

Keywords

• nonclassical diffusion equations
• finite fractal dimension
• pullback attractors